BZPEERPapers, people, evidence and research paths
Menu

Discover

SearchFind papers, people, topics, institutions and opportunities from one place.GraphSee how papers, authors, topics and evidence connect.

Research tools

HomeContinue from the papers, people and topics that matter now.CollectionsTurn saved papers into reading lists, evidence maps and shareable context.ResearchReconstruct the path that led you from search to paper to question.CollaborationMove from a paper, topic or expert request into a focused thread.PublishCreate full-text research articles with metadata, formulas and versions.

Network

ExpertsFind specialists whose work and reviews explain why they can help.CommunitiesJoin research groups organized around papers, topics and shared evidence.

Opportunities

ListingsBrowse roles, calls and collaborations connected to real research context.

Account

Log inReturn to your saved papers, graph views and active threads.Create accountStart saving papers, building a research trail and joining teams.
Log inCreate account

Source author record

Mohammad Ghavamzadeh

Mohammad Ghavamzadeh appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Machine LearningArtificial Intelligencemath.OCComputation and LanguageSystems and ControlComputer VisionData Structures and Algorithmseess.SYInformation RetrievalMultiagent SystemsRobotics

Catalog footprint

What is connected

38works
11topics
4close collaborators

Actions

Connect this record

Log in to claim
Open graphBrowse works

Research graph

See the researcher in context

Open full explorer

Inspect adjacent papers, topics, institutions and collaborators without losing the researcher page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

38 published item(s)

preprint2026arXiv

Bayesian policy gradient and actor-critic algorithms

Policy gradient methods are reinforcement learning algorithms that adapt a parameterized policy by following a performance gradient estimate. Conventional policy gradient methods use Monte-Carlo techniques to estimate the gradient, which tend to have high variance, requiring many samples and resulting in slow convergence. We first propose a Bayesian framework for policy gradient, based on modeling the policy gradient as a Gaussian process. This reduces the number of samples needed to obtain accurate gradient estimates. Moreover, estimates of the natural gradient and a measure of the uncertainty in the gradient estimates, namely, the gradient covariance, are provided at little extra cost. Since the proposed framework considers system trajectories as its basic observable unit, it does not require the dynamics within trajectories to be of any particular form, and can be extended to partially observable problems. On the downside, it cannot exploit the Markov property when the system is Markovian. To address this, we supplement our Bayesian policy gradient framework with a new actor-critic learning model in which a Bayesian class of non-parametric critics, based on Gaussian process temporal difference learning, is used. Such critics model the action-value function as a Gaussian process, allowing Bayes rule to be used to compute the posterior distribution over action-value functions, conditioned on the observed data. Appropriate choices of the policy parameterization and of the prior covariance (kernel) between action-values yield closed-form expressions for the posterior of the gradient of the expected return with respect to the policy parameters. We perform detailed experimental comparisons of the proposed Bayesian policy gradient and actor-critic algorithms with classic Monte-Carlo based policy gradient methods, on a number of reinforcement learning problems.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

MAPLE: Latent Multi-Agent Play for End-to-End Autonomous Driving

Vision-language-action (VLA) models are effective as end-to-end motion planners, but can be brittle when evaluated in closed-loop settings due to being trained under traditional imitation learning framework. Existing closed-loop supervision approaches lack scalability and fail to completely model a reactive environment. We propose MAPLE, a novel framework for reactive, multi-agent rollout of a dynamic driving scenario in the latent space of the VLA model. The ego vehicle and nearby traffic agents are independently controlled over multi-step horizons, while being reactive to other agents in the scene, enabling closed-loop training. MAPLE consists of two training stages: (1) supervised fine-tuning on the latent rollouts based on ground-truth trajectories, followed by (2) reinforcement learning with global and agent -specific rewards that encourage safety, progress, and interaction realism. We further propose diversity rewards that encourage the model to generate planning behaviors that may not be present in logged driving data. Notably, our closed-loop training framework is scalable and does not require external simulators, which can be computationally expensive to run and have limited visual fidelity to the real-world. MAPLE achieves state-of-the-art driving performance on Bench2Drive and demonstrates scalable, closed-loop multi-agent play for robust E2E autonomous driving systems.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Mixture-of-Expert Approach to RL-based Dialogue Management

Despite recent advancements in language models (LMs), their application to dialogue management (DM) problems and ability to carry on rich conversations remain a challenge. We use reinforcement learning (RL) to develop a dialogue agent that avoids being short-sighted (outputting generic utterances) and maximizes overall user satisfaction. Most existing RL approaches to DM train the agent at the word-level, and thus, have to deal with a combinatorially complex action space even for a medium-size vocabulary. As a result, they struggle to produce a successful and engaging dialogue even if they are warm-started with a pre-trained LM. To address this issue, we develop a RL-based DM using a novel mixture of expert language model (MoE-LM) that consists of (i) a LM capable of learning diverse semantics for conversation histories, (ii) a number of {\em specialized} LMs (or experts) capable of generating utterances corresponding to a particular attribute or personality, and (iii) a RL-based DM that performs dialogue planning with the utterances generated by the experts. Our MoE approach provides greater flexibility to generate sensible utterances with different intents and allows RL to focus on conversational-level DM. We compare it with SOTA baselines on open-domain dialogues and demonstrate its effectiveness both in terms of the diversity and sensibility of the generated utterances and the overall DM performance.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Collaborative Multi-agent Stochastic Linear Bandits

We study a collaborative multi-agent stochastic linear bandit setting, where $N$ agents that form a network communicate locally to minimize their overall regret. In this setting, each agent has its own linear bandit problem (its own reward parameter) and the goal is to select the best global action w.r.t. the average of their reward parameters. At each round, each agent proposes an action, and one action is randomly selected and played as the network action. All the agents observe the corresponding rewards of the played actions and use an accelerated consensus procedure to compute an estimate of the average of the rewards obtained by all the agents. We propose a distributed upper confidence bound (UCB) algorithm and prove a high probability bound on its $T$-round regret in which we include a linear growth of regret associated with each communication round. Our regret bound is of order $\mathcal{O}\Big(\sqrt{\frac{T}{N \log(1/|λ_2|)}}\cdot (\log T)^2\Big)$, where $λ_2$ is the second largest (in absolute value) eigenvalue of the communication matrix.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Deep Hierarchy in Bandits

Mean rewards of actions are often correlated. The form of these correlations may be complex and unknown a priori, such as the preferences of a user for recommended products and their categories. To maximize statistical efficiency, it is important to leverage these correlations when learning. We formulate a bandit variant of this problem where the correlations of mean action rewards are represented by a hierarchical Bayesian model with latent variables. Since the hierarchy can have multiple layers, we call it deep. We propose a hierarchical Thompson sampling algorithm (HierTS) for this problem, and show how to implement it efficiently for Gaussian hierarchies. The efficient implementation is possible due to a novel exact hierarchical representation of the posterior, which itself is of independent interest. We use this exact posterior to analyze the Bayes regret of HierTS in Gaussian bandits. Our analysis reflects the structure of the problem, that the regret decreases with the prior width, and also shows that hierarchies reduce the regret by non-constant factors in the number of actions. We confirm these theoretical findings empirically, in both synthetic and real-world experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Feature and Parameter Selection in Stochastic Linear Bandits

We study two model selection settings in stochastic linear bandits (LB). In the first setting, which we refer to as feature selection, the expected reward of the LB problem is in the linear span of at least one of $M$ feature maps (models). In the second setting, the reward parameter of the LB problem is arbitrarily selected from $M$ models represented as (possibly) overlapping balls in $\mathbb R^d$. However, the agent only has access to misspecified models, i.e.,~estimates of the centers and radii of the balls. We refer to this setting as parameter selection. For each setting, we develop and analyze a computationally efficient algorithm that is based on a reduction from bandits to full-information problems. This allows us to obtain regret bounds that are not worse (up to a $\sqrt{\log M}$ factor) than the case where the true model is known. This is the best-reported dependence on the number of models $M$ in these settings. Finally, we empirically show the effectiveness of our algorithms using synthetic and real-world experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Hierarchical Bayesian Bandits

Meta-, multi-task, and federated learning can be all viewed as solving similar tasks, drawn from a distribution that reflects task similarities. We provide a unified view of all these problems, as learning to act in a hierarchical Bayesian bandit. We propose and analyze a natural hierarchical Thompson sampling algorithm (HierTS) for this class of problems. Our regret bounds hold for many variants of the problems, including when the tasks are solved sequentially or in parallel; and show that the regret decreases with a more informative prior. Our proofs rely on a novel total variance decomposition that can be applied beyond our models. Our theory is complemented by experiments, which show that the hierarchy helps with knowledge sharing among the tasks. This confirms that hierarchical Bayesian bandits are a universal and statistically-efficient tool for learning to act with similar bandit tasks.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Multi-Environment Meta-Learning in Stochastic Linear Bandits

In this work we investigate meta-learning (or learning-to-learn) approaches in multi-task linear stochastic bandit problems that can originate from multiple environments. Inspired by the work of [1] on meta-learning in a sequence of linear bandit problems whose parameters are sampled from a single distribution (i.e., a single environment), here we consider the feasibility of meta-learning when task parameters are drawn from a mixture distribution instead. For this problem, we propose a regularized version of the OFUL algorithm that, when trained on tasks with labeled environments, achieves low regret on a new task without requiring knowledge of the environment from which the new task originates. Specifically, our regret bound for the new algorithm captures the effect of environment misclassification and highlights the benefits over learning each task separately or meta-learning without recognition of the distinct mixture components.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Reinforcement Learning of Multi-Domain Dialog Policies Via Action Embeddings

Learning task-oriented dialog policies via reinforcement learning typically requires large amounts of interaction with users, which in practice renders such methods unusable for real-world applications. In order to reduce the data requirements, we propose to leverage data from across different dialog domains, thereby reducing the amount of data required from each given domain. In particular, we propose to learn domain-agnostic action embeddings, which capture general-purpose structure that informs the system how to act given the current dialog context, and are then specialized to a specific domain. We show how this approach is capable of learning with significantly less interaction with users, with a reduction of 35% in the number of dialogs required to learn, and to a higher level of proficiency than training separate policies for each domain on a set of simulated domains.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Thompson Sampling with a Mixture Prior

We study Thompson sampling (TS) in online decision making, where the uncertain environment is sampled from a mixture distribution. This is relevant in multi-task learning, where a learning agent faces different classes of problems. We incorporate this structure in a natural way by initializing TS with a mixture prior, and call the resulting algorithm MixTS. To analyze MixTS, we develop a novel and general proof technique for analyzing the concentration of mixture distributions. We use it to prove Bayes regret bounds for MixTS in both linear bandits and finite-horizon reinforcement learning. Our bounds capture the structure of the prior, depend on the number of mixture components and their widths. We also demonstrate the empirical effectiveness of MixTS in synthetic and real-world experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Policy-Aware Model Learning for Policy Gradient Methods

This paper considers the problem of learning a model in model-based reinforcement learning (MBRL). We examine how the planning module of an MBRL algorithm uses the model, and propose that the model learning module should incorporate the way the planner is going to use the model. This is in contrast to conventional model learning approaches, such as those based on maximum likelihood estimate, that learn a predictive model of the environment without explicitly considering the interaction of the model and the planner. We focus on policy gradient type of planning algorithms and derive new loss functions for model learning that incorporate how the planner uses the model. We call this approach Policy-Aware Model Learning (PAML). We theoretically analyze a generic model-based policy gradient algorithm and provide a convergence guarantee for the optimized policy. We also empirically evaluate PAML on some benchmark problems, showing promising results.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Soft-Robust Algorithms for Batch Reinforcement Learning

In reinforcement learning, robust policies for high-stakes decision-making problems with limited data are usually computed by optimizing the percentile criterion, which minimizes the probability of a catastrophic failure. Unfortunately, such policies are typically overly conservative as the percentile criterion is non-convex, difficult to optimize, and ignores the mean performance. To overcome these shortcomings, we study the soft-robust criterion, which uses risk measures to balance the mean and percentile criterion better. In this paper, we establish the soft-robust criterion's fundamental properties, show that it is NP-hard to optimize, and propose and analyze two algorithms to approximately optimize it. Our theoretical analyses and empirical evaluations demonstrate that our algorithms compute much less conservative solutions than the existing approximate methods for optimizing the percentile-criterion.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Active Model Estimation in Markov Decision Processes

We study the problem of efficient exploration in order to learn an accurate model of an environment, modeled as a Markov decision process (MDP). Efficient exploration in this problem requires the agent to identify the regions in which estimating the model is more difficult and then exploit this knowledge to collect more samples there. In this paper, we formalize this problem, introduce the first algorithm to learn an $ε$-accurate estimate of the dynamics, and provide its sample complexity analysis. While this algorithm enjoys strong guarantees in the large-sample regime, it tends to have a poor performance in early stages of exploration. To address this issue, we propose an algorithm that is based on maximum weighted entropy, a heuristic that stems from common sense and our theoretical analysis. The main idea here is to cover the entire state-action space with the weight proportional to the noise in the transitions. Using a number of simple domains with heterogeneous noise in their transitions, we show that our heuristic-based algorithm outperforms both our original algorithm and the maximum entropy algorithm in the small sample regime, while achieving similar asymptotic performance as that of the original algorithm.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Conservative Exploration in Reinforcement Learning

While learning in an unknown Markov Decision Process (MDP), an agent should trade off exploration to discover new information about the MDP, and exploitation of the current knowledge to maximize the reward. Although the agent will eventually learn a good or optimal policy, there is no guarantee on the quality of the intermediate policies. This lack of control is undesired in real-world applications where a minimum requirement is that the executed policies are guaranteed to perform at least as well as an existing baseline. In this paper, we introduce the notion of conservative exploration for average reward and finite horizon problems. We present two optimistic algorithms that guarantee (w.h.p.) that the conservative constraint is never violated during learning. We derive regret bounds showing that being conservative does not hinder the learning ability of these algorithms.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Control-Aware Representations for Model-based Reinforcement Learning

A major challenge in modern reinforcement learning (RL) is efficient control of dynamical systems from high-dimensional sensory observations. Learning controllable embedding (LCE) is a promising approach that addresses this challenge by embedding the observations into a lower-dimensional latent space, estimating the latent dynamics, and utilizing it to perform control in the latent space. Two important questions in this area are how to learn a representation that is amenable to the control problem at hand, and how to achieve an end-to-end framework for representation learning and control. In this paper, we take a few steps towards addressing these questions. We first formulate a LCE model to learn representations that are suitable to be used by a policy iteration style algorithm in the latent space. We call this model control-aware representation learning (CARL). We derive a loss function for CARL that has close connection to the prediction, consistency, and curvature (PCC) principle for representation learning. We derive three implementations of CARL. In the offline implementation, we replace the locally-linear control algorithm (e.g.,~iLQR) used by the existing LCE methods with a RL algorithm, namely model-based soft actor-critic, and show that it results in significant improvement. In online CARL, we interleave representation learning and control, and demonstrate further gain in performance. Finally, we propose value-guided CARL, a variation in which we optimize a weighted version of the CARL loss function, where the weights depend on the TD-error of the current policy. We evaluate the proposed algorithms by extensive experiments on benchmark tasks and compare them with several LCE baselines.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Finite-Sample Analysis of Proximal Gradient TD Algorithms

In this paper, we analyze the convergence rate of the gradient temporal difference learning (GTD) family of algorithms. Previous analyses of this class of algorithms use ODE techniques to prove asymptotic convergence, and to the best of our knowledge, no finite-sample analysis has been done. Moreover, there has been not much work on finite-sample analysis for convergent off-policy reinforcement learning algorithms. In this paper, we formulate GTD methods as stochastic gradient algorithms w.r.t.~a primal-dual saddle-point objective function, and then conduct a saddle-point error analysis to obtain finite-sample bounds on their performance. Two revised algorithms are also proposed, namely projected GTD2 and GTD2-MP, which offer improved convergence guarantees and acceleration, respectively. The results of our theoretical analysis show that the GTD family of algorithms are indeed comparable to the existing LSTD methods in off-policy learning scenarios.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Improved Algorithms for Conservative Exploration in Bandits

In many fields such as digital marketing, healthcare, finance, and robotics, it is common to have a well-tested and reliable baseline policy running in production (e.g., a recommender system). Nonetheless, the baseline policy is often suboptimal. In this case, it is desirable to deploy online learning algorithms (e.g., a multi-armed bandit algorithm) that interact with the system to learn a better/optimal policy under the constraint that during the learning process the performance is almost never worse than the performance of the baseline itself. In this paper, we study the conservative learning problem in the contextual linear bandit setting and introduce a novel algorithm, the Conservative Constrained LinUCB (CLUCB2). We derive regret bounds for CLUCB2 that match existing results and empirically show that it outperforms state-of-the-art conservative bandit algorithms in a number of synthetic and real-world problems. Finally, we consider a more realistic constraint where the performance is verified only at predefined checkpoints (instead of at every step) and show how this relaxed constraint favorably impacts the regret and empirical performance of CLUCB2.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Multi-step Greedy Reinforcement Learning Algorithms

Multi-step greedy policies have been extensively used in model-based reinforcement learning (RL), both when a model of the environment is available (e.g.,~in the game of Go) and when it is learned. In this paper, we explore their benefits in model-free RL, when employed using multi-step dynamic programming algorithms: $κ$-Policy Iteration ($κ$-PI) and $κ$-Value Iteration ($κ$-VI). These methods iteratively compute the next policy ($κ$-PI) and value function ($κ$-VI) by solving a surrogate decision problem with a shaped reward and a smaller discount factor. We derive model-free RL algorithms based on $κ$-PI and $κ$-VI in which the surrogate problem can be solved by any discrete or continuous action RL method, such as DQN and TRPO. We identify the importance of a hyper-parameter that controls the extent to which the surrogate problem is solved and suggest a way to set this parameter. When evaluated on a range of Atari and MuJoCo benchmark tasks, our results indicate that for the right range of $κ$, our algorithms outperform DQN and TRPO. This shows that our multi-step greedy algorithms are general enough to be applied over any existing RL algorithm and can significantly improve its performance.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Prediction, Consistency, Curvature: Representation Learning for Locally-Linear Control

Many real-world sequential decision-making problems can be formulated as optimal control with high-dimensional observations and unknown dynamics. A promising approach is to embed the high-dimensional observations into a lower-dimensional latent representation space, estimate the latent dynamics model, then utilize this model for control in the latent space. An important open question is how to learn a representation that is amenable to existing control algorithms? In this paper, we focus on learning representations for locally-linear control algorithms, such as iterative LQR (iLQR). By formulating and analyzing the representation learning problem from an optimal control perspective, we establish three underlying principles that the learned representation should comprise: 1) accurate prediction in the observation space, 2) consistency between latent and observation space dynamics, and 3) low curvature in the latent space transitions. These principles naturally correspond to a loss function that consists of three terms: prediction, consistency, and curvature (PCC). Crucially, to make PCC tractable, we derive an amortized variational bound for the PCC loss function. Extensive experiments on benchmark domains demonstrate that the new variational-PCC learning algorithm benefits from significantly more stable and reproducible training, and leads to superior control performance. Further ablation studies give support to the importance of all three PCC components for learning a good latent space for control.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Predictive Coding for Locally-Linear Control

High-dimensional observations and unknown dynamics are major challenges when applying optimal control to many real-world decision making tasks. The Learning Controllable Embedding (LCE) framework addresses these challenges by embedding the observations into a lower dimensional latent space, estimating the latent dynamics, and then performing control directly in the latent space. To ensure the learned latent dynamics are predictive of next-observations, all existing LCE approaches decode back into the observation space and explicitly perform next-observation prediction---a challenging high-dimensional task that furthermore introduces a large number of nuisance parameters (i.e., the decoder) which are discarded during control. In this paper, we propose a novel information-theoretic LCE approach and show theoretically that explicit next-observation prediction can be replaced with predictive coding. We then use predictive coding to develop a decoder-free LCE model whose latent dynamics are amenable to locally-linear control. Extensive experiments on benchmark tasks show that our model reliably learns a controllable latent space that leads to superior performance when compared with state-of-the-art LCE baselines.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Proximal Gradient Temporal Difference Learning: Stable Reinforcement Learning with Polynomial Sample Complexity

In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD) reinforcement learning methods can be formally derived, not by starting from their original objective functions, as previously attempted, but rather from a primal-dual saddle-point objective function. We also conduct a saddle-point error analysis to obtain finite-sample bounds on their performance. Previous analyses of this class of algorithms use stochastic approximation techniques to prove asymptotic convergence, and do not provide any finite-sample analysis. We also propose an accelerated algorithm, called GTD2-MP, that uses proximal ``mirror maps'' to yield an improved convergence rate. The results of our theoretical analysis imply that the GTD family of algorithms are comparable and may indeed be preferred over existing least squares TD methods for off-policy learning, due to their linear complexity. We provide experimental results showing the improved performance of our accelerated gradient TD methods.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Stochastic Bandits with Linear Constraints

We study a constrained contextual linear bandit setting, where the goal of the agent is to produce a sequence of policies, whose expected cumulative reward over the course of $T$ rounds is maximum, and each has an expected cost below a certain threshold $τ$. We propose an upper-confidence bound algorithm for this problem, called optimistic pessimistic linear bandit (OPLB), and prove an $\widetilde{\mathcal{O}}(\frac{d\sqrt{T}}{τ-c_0})$ bound on its $T$-round regret, where the denominator is the difference between the constraint threshold and the cost of a known feasible action. We further specialize our results to multi-armed bandits and propose a computationally efficient algorithm for this setting. We prove a regret bound of $\widetilde{\mathcal{O}}(\frac{\sqrt{KT}}{τ- c_0})$ for this algorithm in $K$-armed bandits, which is a $\sqrt{K}$ improvement over the regret bound we obtain by simply casting multi-armed bandits as an instance of contextual linear bandits and using the regret bound of OPLB. We also prove a lower-bound for the problem studied in the paper and provide simulations to validate our theoretical results.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Variance-Reduced Off-Policy Memory-Efficient Policy Search

Off-policy policy optimization is a challenging problem in reinforcement learning (RL). The algorithms designed for this problem often suffer from high variance in their estimators, which results in poor sample efficiency, and have issues with convergence. A few variance-reduced on-policy policy gradient algorithms have been recently proposed that use methods from stochastic optimization to reduce the variance of the gradient estimate in the REINFORCE algorithm. However, these algorithms are not designed for the off-policy setting and are memory-inefficient, since they need to collect and store a large ``reference'' batch of samples from time to time. To achieve variance-reduced off-policy-stable policy optimization, we propose an algorithm family that is memory-efficient, stochastically variance-reduced, and capable of learning from off-policy samples. Empirical studies validate the effectiveness of the proposed approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Variational Model-based Policy Optimization

Model-based reinforcement learning (RL) algorithms allow us to combine model-generated data with those collected from interaction with the real system in order to alleviate the data efficiency problem in RL. However, designing such algorithms is often challenging because the bias in simulated data may overshadow the ease of data generation. A potential solution to this challenge is to jointly learn and improve model and policy using a universal objective function. In this paper, we leverage the connection between RL and probabilistic inference, and formulate such an objective function as a variational lower-bound of a log-likelihood. This allows us to use expectation maximization (EM) and iteratively fix a baseline policy and learn a variational distribution, consisting of a model and a policy (E-step), followed by improving the baseline policy given the learned variational distribution (M-step). We propose model-based and model-free policy iteration (actor-critic) style algorithms for the E-step and show how the variational distribution learned by them can be used to optimize the M-step in a fully model-based fashion. Our experiments on a number of continuous control tasks show that despite being more complex, our model-based (E-step) algorithm, called {\em variational model-based policy optimization} (VMBPO), is more sample-efficient and robust to hyper-parameter tuning than its model-free (E-step) counterpart. Using the same control tasks, we also compare VMBPO with several state-of-the-art model-based and model-free RL algorithms and show its sample efficiency and performance.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Bayesian Reinforcement Learning: A Survey

Bayesian methods for machine learning have been widely investigated, yielding principled methods for incorporating prior information into inference algorithms. In this survey, we provide an in-depth review of the role of Bayesian methods for the reinforcement learning (RL) paradigm. The major incentives for incorporating Bayesian reasoning in RL are: 1) it provides an elegant approach to action-selection (exploration/exploitation) as a function of the uncertainty in learning; and 2) it provides a machinery to incorporate prior knowledge into the algorithms. We first discuss models and methods for Bayesian inference in the simple single-step Bandit model. We then review the extensive recent literature on Bayesian methods for model-based RL, where prior information can be expressed on the parameters of the Markov model. We also present Bayesian methods for model-free RL, where priors are expressed over the value function or policy class. The objective of the paper is to provide a comprehensive survey on Bayesian RL algorithms and their theoretical and empirical properties.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Graphical Model Sketch

Structured high-cardinality data arises in many domains, and poses a major challenge for both modeling and inference. Graphical models are a popular approach to modeling structured data but they are unsuitable for high-cardinality variables. The count-min (CM) sketch is a popular approach to estimating probabilities in high-cardinality data but it does not scale well beyond a few variables. In this work, we bring together the ideas of graphical models and count sketches; and propose and analyze several approaches to estimating probabilities in structured high-cardinality streams of data. The key idea of our approximations is to use the structure of a graphical model and approximately estimate its factors by "sketches", which hash high-cardinality variables using random projections. Our approximations are computationally efficient and their space complexity is independent of the cardinality of variables. Our error bounds are multiplicative and significantly improve upon those of the CM sketch, a state-of-the-art approach to estimating probabilities in streams. We evaluate our approximations on synthetic and real-world problems, and report an order of magnitude improvements over the CM sketch.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Personalized Advertisement Recommendation: A Ranking Approach to Address the Ubiquitous Click Sparsity Problem

We study the problem of personalized advertisement recommendation (PAR), which consist of a user visiting a system (website) and the system displaying one of $K$ ads to the user. The system uses an internal ad recommendation policy to map the user's profile (context) to one of the ads. The user either clicks or ignores the ad and correspondingly, the system updates its recommendation policy. PAR problem is usually tackled by scalable \emph{contextual bandit} algorithms, where the policies are generally based on classifiers. A practical problem in PAR is extreme click sparsity, due to very few users actually clicking on ads. We systematically study the drawback of using contextual bandit algorithms based on classifier-based policies, in face of extreme click sparsity. We then suggest an alternate policy, based on rankers, learnt by optimizing the Area Under the Curve (AUC) ranking loss, which can significantly alleviate the problem of click sparsity. We conduct extensive experiments on public datasets, as well as three industry proprietary datasets, to illustrate the improvement in click-through-rate (CTR) obtained by using the ranker-based policy over classifier-based policies.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Safe Policy Improvement by Minimizing Robust Baseline Regret

An important problem in sequential decision-making under uncertainty is to use limited data to compute a safe policy, i.e., a policy that is guaranteed to perform at least as well as a given baseline strategy. In this paper, we develop and analyze a new model-based approach to compute a safe policy when we have access to an inaccurate dynamics model of the system with known accuracy guarantees. Our proposed robust method uses this (inaccurate) model to directly minimize the (negative) regret w.r.t. the baseline policy. Contrary to the existing approaches, minimizing the regret allows one to improve the baseline policy in states with accurate dynamics and seamlessly fall back to the baseline policy, otherwise. We show that our formulation is NP-hard and propose an approximate algorithm. Our empirical results on several domains show that even this relatively simple approximate algorithm can significantly outperform standard approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

A Generalized Kernel Approach to Structured Output Learning

We study the problem of structured output learning from a regression perspective. We first provide a general formulation of the kernel dependency estimation (KDE) problem using operator-valued kernels. We show that some of the existing formulations of this problem are special cases of our framework. We then propose a covariance-based operator-valued kernel that allows us to take into account the structure of the kernel feature space. This kernel operates on the output space and encodes the interactions between the outputs without any reference to the input space. To address this issue, we introduce a variant of our KDE method based on the conditional covariance operator that in addition to the correlation between the outputs takes into account the effects of the input variables. Finally, we evaluate the performance of our KDE approach using both covariance and conditional covariance kernels on two structured output problems, and compare it to the state-of-the-art kernel-based structured output regression methods.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Policy Gradient for Coherent Risk Measures

Several authors have recently developed risk-sensitive policy gradient methods that augment the standard expected cost minimization problem with a measure of variability in cost. These studies have focused on specific risk-measures, such as the variance or conditional value at risk (CVaR). In this work, we extend the policy gradient method to the whole class of coherent risk measures, which is widely accepted in finance and operations research, among other fields. We consider both static and time-consistent dynamic risk measures. For static risk measures, our approach is in the spirit of policy gradient algorithms and combines a standard sampling approach with convex programming. For dynamic risk measures, our approach is actor-critic style and involves explicit approximation of value function. Most importantly, our contribution presents a unified approach to risk-sensitive reinforcement learning that generalizes and extends previous results.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Robust Policy Optimization with Baseline Guarantees

Our goal is to compute a policy that guarantees improved return over a baseline policy even when the available MDP model is inaccurate. The inaccurate model may be constructed, for example, by system identification techniques when the true model is inaccessible. When the modeling error is large, the standard solution to the constructed model has no performance guarantees with respect to the true model. In this paper we develop algorithms that provide such performance guarantees and show a trade-off between their complexity and conservatism. Our novel model-based safe policy search algorithms leverage recent advances in robust optimization techniques. Furthermore we illustrate the effectiveness of these algorithms using a numerical example.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Upper-Confidence-Bound Algorithms for Active Learning in Multi-Armed Bandits

In this paper, we study the problem of estimating uniformly well the mean values of several distributions given a finite budget of samples. If the variance of the distributions were known, one could design an optimal sampling strategy by collecting a number of independent samples per distribution that is proportional to their variance. However, in the more realistic case where the distributions are not known in advance, one needs to design adaptive sampling strategies in order to select which distribution to sample from according to the previously observed samples. We describe two strategies based on pulling the distributions a number of times that is proportional to a high-probability upper-confidence-bound on their variance (built from previous observed samples) and report a finite-sample performance analysis on the excess estimation error compared to the optimal allocation. We show that the performance of these allocation strategies depends not only on the variances but also on the full shape of the distributions.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Variance-Constrained Actor-Critic Algorithms for Discounted and Average Reward MDPs

In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in rewards in addition to maximizing a standard criterion. Variance related risk measures are among the most common risk-sensitive criteria in finance and operations research. However, optimizing many such criteria is known to be a hard problem. In this paper, we consider both discounted and average reward Markov decision processes. For each formulation, we first define a measure of variability for a policy, which in turn gives us a set of risk-sensitive criteria to optimize. For each of these criteria, we derive a formula for computing its gradient. We then devise actor-critic algorithms that operate on three timescales - a TD critic on the fastest timescale, a policy gradient (actor) on the intermediate timescale, and a dual ascent for Lagrange multipliers on the slowest timescale. In the discounted setting, we point out the difficulty in estimating the gradient of the variance of the return and incorporate simultaneous perturbation approaches to alleviate this. The average setting, on the other hand, allows for an actor update using compatible features to estimate the gradient of the variance. We establish the convergence of our algorithms to locally risk-sensitive optimal policies. Finally, we demonstrate the usefulness of our algorithms in a traffic signal control application.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Algorithms for CVaR Optimization in MDPs

In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in costs in addition to minimizing a standard criterion. Conditional value-at-risk (CVaR) is a relatively new risk measure that addresses some of the shortcomings of the well-known variance-related risk measures, and because of its computational efficiencies has gained popularity in finance and operations research. In this paper, we consider the mean-CVaR optimization problem in MDPs. We first derive a formula for computing the gradient of this risk-sensitive objective function. We then devise policy gradient and actor-critic algorithms that each uses a specific method to estimate this gradient and updates the policy parameters in the descent direction. We establish the convergence of our algorithms to locally risk-sensitive optimal policies. Finally, we demonstrate the usefulness of our algorithms in an optimal stopping problem.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Classification-based Approximate Policy Iteration: Experiments and Extended Discussions

Tackling large approximate dynamic programming or reinforcement learning problems requires methods that can exploit regularities, or intrinsic structure, of the problem in hand. Most current methods are geared towards exploiting the regularities of either the value function or the policy. We introduce a general classification-based approximate policy iteration (CAPI) framework, which encompasses a large class of algorithms that can exploit regularities of both the value function and the policy space, depending on what is advantageous. This framework has two main components: a generic value function estimator and a classifier that learns a policy based on the estimated value function. We establish theoretical guarantees for the sample complexity of CAPI-style algorithms, which allow the policy evaluation step to be performed by a wide variety of algorithms (including temporal-difference-style methods), and can handle nonparametric representations of policies. Our bounds on the estimation error of the performance loss are tighter than existing results. We also illustrate this approach empirically on several problems, including a large HIV control task.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Constrained Stochastic Optimal Control with a Baseline Performance Guarantee

In this paper, we show how a simulated Markov decision process (MDP) built by the so-called \emph{baseline} policies, can be used to compute a different policy, namely the \emph{simulated optimal} policy, for which the performance of this policy is guaranteed to be better than the baseline policy in the real environment. This technique has immense applications in fields such as news recommendation systems, health care diagnosis and digital online marketing. Our proposed algorithm iteratively solves for a "good" policy in the simulated MDP in an offline setting. Furthermore, we provide a performance bound on sub-optimality for the control policy generated by the proposed algorithm.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

A Dantzig Selector Approach to Temporal Difference Learning

LSTD is a popular algorithm for value function approximation. Whenever the number of features is larger than the number of samples, it must be paired with some form of regularization. In particular, L1-regularization methods tend to perform feature selection by promoting sparsity, and thus, are well-suited for high-dimensional problems. However, since LSTD is not a simple regression algorithm, but it solves a fixed--point problem, its integration with L1-regularization is not straightforward and might come with some drawbacks (e.g., the P-matrix assumption for LASSO-TD). In this paper, we introduce a novel algorithm obtained by integrating LSTD with the Dantzig Selector. We investigate the performance of the proposed algorithm and its relationship with the existing regularized approaches, and show how it addresses some of their drawbacks.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Approximate Modified Policy Iteration

Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three implementations of approximate MPI (AMPI) that are extensions of well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide error propagation analyses that unify those for approximate policy and value iteration. On the last classification-based implementation, we develop a finite-sample analysis that shows that MPI's main parameter allows to control the balance between the estimation error of the classifier and the overall value function approximation.

0 citations0 reviewsNo code linkedOpen access