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Researcher profile

Aldo Pacchiano

Aldo Pacchiano contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningArtificial Intelligencemath.OCNeural and Evolutionary ComputingComputation and LanguageData Structures and AlgorithmsRobotics

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Published work

21 published item(s)

preprint2026arXiv

Multiple-policy Evaluation via Density Estimation

We study the multiple-policy evaluation problem where we are given a set of $K$ policies and the goal is to evaluate their performance (expected total reward over a fixed horizon) to an accuracy $ε$ with probability at least $1-δ$. We propose an algorithm named $\mathrm{CAESAR}$ for this problem. Our approach is based on computing an approximate optimal offline sampling distribution and using the data sampled from it to perform the simultaneous estimation of the policy values. $\mathrm{CAESAR}$ has two phases. In the first we produce coarse estimates of the visitation distributions of the target policies at a low order sample complexity rate that scales with $\tilde{O}(\frac{1}ε)$. In the second phase, we approximate the optimal offline sampling distribution and compute the importance weighting ratios for all target policies by minimizing a step-wise quadratic loss function inspired by the DualDICE \cite{nachum2019dualdice} objective. Up to low order and logarithmic terms $\mathrm{CAESAR}$ achieves a sample complexity $\tilde{O}\left(\frac{H^4}{ε^2}\sum_{h=1}^H\max_{k\in[K]}\sum_{s,a}\frac{(d_h^{π^k}(s,a))^2}{μ^*_h(s,a)}\right)$, where $d^π$ is the visitation distribution of policy $π$, $μ^*$ is the optimal sampling distribution, and $H$ is the horizon.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

When Less is Enough: Efficient Inference via Collaborative Reasoning

In this work, we introduce DUET (Dual-model Efficient Two-stage inference), a collaborative inference framework in which a capable model and a lightweight model work together to solve a task. Relying on a single large model to perform end-to-end reasoning and prediction often incurs substantial inference cost. In contrast, DUET decomposes inference into two stages: the capable model produces a reasoning signal, and the lightweight model interprets this signal to generate the final answer, allowing reasoning-intensive computation to be handled by the capable model while non-reasoning-intensive components are delegated to the lightweight model without sacrificing task performance. To achieve this objective, we propose a length-penalized joint training objective that encourages the capable model to transmit only the information that is sufficient for the lightweight model to solve the task. As a result, DUET maintains strong reasoning performance with substantially lower inference cost than end-to-end inference using a large model alone, saving up to 60% of the large model's output tokens on challenging reasoning benchmarks, including AIME and GPQA.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Best of Both Worlds Model Selection

We study the problem of model selection in bandit scenarios in the presence of nested policy classes, with the goal of obtaining simultaneous adversarial and stochastic ("best of both worlds") high-probability regret guarantees. Our approach requires that each base learner comes with a candidate regret bound that may or may not hold, while our meta algorithm plays each base learner according to a schedule that keeps the base learner's candidate regret bounds balanced until they are detected to violate their guarantees. We develop careful mis-specification tests specifically designed to blend the above model selection criterion with the ability to leverage the (potentially benign) nature of the environment. We recover the model selection guarantees of the CORRAL algorithm for adversarial environments, but with the additional benefit of achieving high probability regret bounds, specifically in the case of nested adversarial linear bandits. More importantly, our model selection results also hold simultaneously in stochastic environments under gap assumptions. These are the first theoretical results that achieve best of both world (stochastic and adversarial) guarantees while performing model selection in (linear) bandit scenarios.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Joint Representation Training in Sequential Tasks with Shared Structure

Classical theory in reinforcement learning (RL) predominantly focuses on the single task setting, where an agent learns to solve a task through trial-and-error experience, given access to data only from that task. However, many recent empirical works have demonstrated the significant practical benefits of leveraging a joint representation trained across multiple, related tasks. In this work we theoretically analyze such a setting, formalizing the concept of task relatedness as a shared state-action representation that admits linear dynamics in all the tasks. We introduce the Shared-MatrixRL algorithm for the setting of Multitask MatrixRL. In the presence of $P$ episodic tasks of dimension $d$ sharing a joint $r \ll d$ low-dimensional representation, we show the regret on the the $P$ tasks can be improved from $O(PHd\sqrt{NH})$ to $O((Hd\sqrt{rP} + HP\sqrt{rd})\sqrt{NH})$ over $N$ episodes of horizon $H$. These gains coincide with those observed in other linear models in contextual bandits and RL. In contrast with previous work that have studied multi task RL in other function approximation models, we show that in the presence of bilinear optimization oracle and finite state action spaces there exists a computationally efficient algorithm for multitask MatrixRL via a reduction to quadratic programming. We also develop a simple technique to shave off a $\sqrt{H}$ factor from the regret upper bounds of some episodic linear problems.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Meta Learning MDPs with Linear Transition Models

We study meta-learning in Markov Decision Processes (MDP) with linear transition models in the undiscounted episodic setting. Under a task sharedness metric based on model proximity we study task families characterized by a distribution over models specified by a bias term and a variance component. We then propose BUC-MatrixRL, a version of the UC-Matrix RL algorithm, and show it can meaningfully leverage a set of sampled training tasks to quickly solve a test task sampled from the same task distribution by learning an estimator of the bias parameter of the task distribution. The analysis leverages and extends results in the learning to learn linear regression and linear bandit setting to the more general case of MDP's with linear transition models. We prove that compared to learning the tasks in isolation, BUC-Matrix RL provides significant improvements in the transfer regret for high bias low variance task distributions.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

On the Theory of Reinforcement Learning with Once-per-Episode Feedback

We study a theory of reinforcement learning (RL) in which the learner receives binary feedback only once at the end of an episode. While this is an extreme test case for theory, it is also arguably more representative of real-world applications than the traditional requirement in RL practice that the learner receive feedback at every time step. Indeed, in many real-world applications of reinforcement learning, such as self-driving cars and robotics, it is easier to evaluate whether a learner's complete trajectory was either "good" or "bad," but harder to provide a reward signal at each step. To show that learning is possible in this more challenging setting, we study the case where trajectory labels are generated by an unknown parametric model, and provide a statistically and computationally efficient algorithm that achieves sublinear regret.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Online Nonsubmodular Minimization with Delayed Costs: From Full Information to Bandit Feedback

Motivated by applications to online learning in sparse estimation and Bayesian optimization, we consider the problem of online unconstrained nonsubmodular minimization with delayed costs in both full information and bandit feedback settings. In contrast to previous works on online unconstrained submodular minimization, we focus on a class of nonsubmodular functions with special structure, and prove regret guarantees for several variants of the online and approximate online bandit gradient descent algorithms in static and delayed scenarios. We derive bounds for the agent's regret in the full information and bandit feedback setting, even if the delay between choosing a decision and receiving the incurred cost is unbounded. Key to our approach is the notion of $(α, β)$-regret and the extension of the generic convex relaxation model from~\citet{El-2020-Optimal}, the analysis of which is of independent interest. We conduct and showcase several simulation studies to demonstrate the efficacy of our algorithms.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Tactical Optimism and Pessimism for Deep Reinforcement Learning

In recent years, deep off-policy actor-critic algorithms have become a dominant approach to reinforcement learning for continuous control. One of the primary drivers of this improved performance is the use of pessimistic value updates to address function approximation errors, which previously led to disappointing performance. However, a direct consequence of pessimism is reduced exploration, running counter to theoretical support for the efficacy of optimism in the face of uncertainty. So which approach is best? In this work, we show that the most effective degree of optimism can vary both across tasks and over the course of learning. Inspired by this insight, we introduce a novel deep actor-critic framework, Tactical Optimistic and Pessimistic (TOP) estimation, which switches between optimistic and pessimistic value learning online. This is achieved by formulating the selection as a multi-arm bandit problem. We show in a series of continuous control tasks that TOP outperforms existing methods which rely on a fixed degree of optimism, setting a new state of the art in challenging pixel-based environments. Since our changes are simple to implement, we believe these insights can easily be incorporated into a multitude of off-policy algorithms.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Towards an Understanding of Default Policies in Multitask Policy Optimization

Much of the recent success of deep reinforcement learning has been driven by regularized policy optimization (RPO) algorithms with strong performance across multiple domains. In this family of methods, agents are trained to maximize cumulative reward while penalizing deviation in behavior from some reference, or default policy. In addition to empirical success, there is a strong theoretical foundation for understanding RPO methods applied to single tasks, with connections to natural gradient, trust region, and variational approaches. However, there is limited formal understanding of desirable properties for default policies in the multitask setting, an increasingly important domain as the field shifts towards training more generally capable agents. Here, we take a first step towards filling this gap by formally linking the quality of the default policy to its effect on optimization. Using these results, we then derive a principled RPO algorithm for multitask learning with strong performance guarantees.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Fairness with Continuous Optimal Transport

Whilst optimal transport (OT) is increasingly being recognized as a powerful and flexible approach for dealing with fairness issues, current OT fairness methods are confined to the use of discrete OT. In this paper, we leverage recent advances from the OT literature to introduce a stochastic-gradient fairness method based on a dual formulation of continuous OT. We show that this method gives superior performance to discrete OT methods when little data is available to solve the OT problem, and similar performance otherwise. We also show that both continuous and discrete OT methods are able to continually adjust the model parameters to adapt to different levels of unfairness that might occur in real-world applications of ML systems.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Accelerated Message Passing for Entropy-Regularized MAP Inference

Maximum a posteriori (MAP) inference in discrete-valued Markov random fields is a fundamental problem in machine learning that involves identifying the most likely configuration of random variables given a distribution. Due to the difficulty of this combinatorial problem, linear programming (LP) relaxations are commonly used to derive specialized message passing algorithms that are often interpreted as coordinate descent on the dual LP. To achieve more desirable computational properties, a number of methods regularize the LP with an entropy term, leading to a class of smooth message passing algorithms with convergence guarantees. In this paper, we present randomized methods for accelerating these algorithms by leveraging techniques that underlie classical accelerated gradient methods. The proposed algorithms incorporate the familiar steps of standard smooth message passing algorithms, which can be viewed as coordinate minimization steps. We show that these accelerated variants achieve faster rates for finding $ε$-optimal points of the unregularized problem, and, when the LP is tight, we prove that the proposed algorithms recover the true MAP solution in fewer iterations than standard message passing algorithms.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Convergence Rates of Smooth Message Passing with Rounding in Entropy-Regularized MAP Inference

Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely configuration of the discrete-valued model. Linear programming (LP) relaxations in the Sherali-Adams hierarchy are widely used to attempt to solve this problem, and smooth message passing algorithms have been proposed to solve regularized versions of these LPs with great success. This paper leverages recent work in entropy-regularized LPs to analyze convergence rates of a class of edge-based smooth message passing algorithms to $ε$-optimality in the relaxation. With an appropriately chosen regularization constant, we present a theoretical guarantee on the number of iterations sufficient to recover the true integral MAP solution when the LP is tight and the solution is unique.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

ES-MAML: Simple Hessian-Free Meta Learning

We introduce ES-MAML, a new framework for solving the model agnostic meta learning (MAML) problem based on Evolution Strategies (ES). Existing algorithms for MAML are based on policy gradients, and incur significant difficulties when attempting to estimate second derivatives using backpropagation on stochastic policies. We show how ES can be applied to MAML to obtain an algorithm which avoids the problem of estimating second derivatives, and is also conceptually simple and easy to implement. Moreover, ES-MAML can handle new types of nonsmooth adaptation operators, and other techniques for improving performance and estimation of ES methods become applicable. We show empirically that ES-MAML is competitive with existing methods and often yields better adaptation with fewer queries.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Gen-Oja: A Two-time-scale approach for Streaming CCA

In this paper, we study the problems of principal Generalized Eigenvector computation and Canonical Correlation Analysis in the stochastic setting. We propose a simple and efficient algorithm, Gen-Oja, for these problems. We prove the global convergence of our algorithm, borrowing ideas from the theory of fast-mixing Markov chains and two-time-scale stochastic approximation, showing that it achieves the optimal rate of convergence. In the process, we develop tools for understanding stochastic processes with Markovian noise which might be of independent interest.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Learning to Score Behaviors for Guided Policy Optimization

We introduce a new approach for comparing reinforcement learning policies, using Wasserstein distances (WDs) in a newly defined latent behavioral space. We show that by utilizing the dual formulation of the WD, we can learn score functions over policy behaviors that can in turn be used to lead policy optimization towards (or away from) (un)desired behaviors. Combined with smoothed WDs, the dual formulation allows us to devise efficient algorithms that take stochastic gradient descent steps through WD regularizers. We incorporate these regularizers into two novel on-policy algorithms, Behavior-Guided Policy Gradient and Behavior-Guided Evolution Strategies, which we demonstrate can outperform existing methods in a variety of challenging environments. We also provide an open source demo.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

On Thompson Sampling with Langevin Algorithms

Thompson sampling for multi-armed bandit problems is known to enjoy favorable performance in both theory and practice. However, it suffers from a significant limitation computationally, arising from the need for samples from posterior distributions at every iteration. We propose two Markov Chain Monte Carlo (MCMC) methods tailored to Thompson sampling to address this issue. We construct quickly converging Langevin algorithms to generate approximate samples that have accuracy guarantees, and we leverage novel posterior concentration rates to analyze the regret of the resulting approximate Thompson sampling algorithm. Further, we specify the necessary hyperparameters for the MCMC procedure to guarantee optimal instance-dependent frequentist regret while having low computational complexity. In particular, our algorithms take advantage of both posterior concentration and a sample reuse mechanism to ensure that only a constant number of iterations and a constant amount of data is needed in each round. The resulting approximate Thompson sampling algorithm has logarithmic regret and its computational complexity does not scale with the time horizon of the algorithm.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Ready Policy One: World Building Through Active Learning

Model-Based Reinforcement Learning (MBRL) offers a promising direction for sample efficient learning, often achieving state of the art results for continuous control tasks. However, many existing MBRL methods rely on combining greedy policies with exploration heuristics, and even those which utilize principled exploration bonuses construct dual objectives in an ad hoc fashion. In this paper we introduce Ready Policy One (RP1), a framework that views MBRL as an active learning problem, where we aim to improve the world model in the fewest samples possible. RP1 achieves this by utilizing a hybrid objective function, which crucially adapts during optimization, allowing the algorithm to trade off reward v.s. exploration at different stages of learning. In addition, we introduce a principled mechanism to terminate sample collection once we have a rich enough trajectory batch to improve the model. We rigorously evaluate our method on a variety of continuous control tasks, and demonstrate statistically significant gains over existing approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Regret Balancing for Bandit and RL Model Selection

We consider model selection in stochastic bandit and reinforcement learning problems. Given a set of base learning algorithms, an effective model selection strategy adapts to the best learning algorithm in an online fashion. We show that by estimating the regret of each algorithm and playing the algorithms such that all empirical regrets are ensured to be of the same order, the overall regret balancing strategy achieves a regret that is close to the regret of the optimal base algorithm. Our strategy requires an upper bound on the optimal base regret as input, and the performance of the strategy depends on the tightness of the upper bound. We show that having this prior knowledge is necessary in order to achieve a near-optimal regret. Further, we show that any near-optimal model selection strategy implicitly performs a form of regret balancing.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Robustness Guarantees for Mode Estimation with an Application to Bandits

Mode estimation is a classical problem in statistics with a wide range of applications in machine learning. Despite this, there is little understanding in its robustness properties under possibly adversarial data contamination. In this paper, we give precise robustness guarantees as well as privacy guarantees under simple randomization. We then introduce a theory for multi-armed bandits where the values are the modes of the reward distributions instead of the mean. We prove regret guarantees for the problems of top arm identification, top m-arms identification, contextual modal bandits, and infinite continuous arms top arm recovery. We show in simulations that our algorithms are robust to perturbation of the arms by adversarial noise sequences, thus rendering modal bandits an attractive choice in situations where the rewards may have outliers or adversarial corruptions.

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

Stochastic Flows and Geometric Optimization on the Orthogonal Group

We present a new class of stochastic, geometrically-driven optimization algorithms on the orthogonal group $O(d)$ and naturally reductive homogeneous manifolds obtained from the action of the rotation group $SO(d)$. We theoretically and experimentally demonstrate that our methods can be applied in various fields of machine learning including deep, convolutional and recurrent neural networks, reinforcement learning, normalizing flows and metric learning. We show an intriguing connection between efficient stochastic optimization on the orthogonal group and graph theory (e.g. matching problem, partition functions over graphs, graph-coloring). We leverage the theory of Lie groups and provide theoretical results for the designed class of algorithms. We demonstrate broad applicability of our methods by showing strong performance on the seemingly unrelated tasks of learning world models to obtain stable policies for the most difficult $\mathrm{Humanoid}$ agent from $\mathrm{OpenAI}$ $\mathrm{Gym}$ and improving convolutional neural networks.

0 citations0 reviewsNo code linkedOpen access