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Alexandre Proutiere

Alexandre Proutiere contributes to research discovery and scholarly infrastructure.

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Published work

9 published item(s)

preprint2026arXiv

Switching Successor Measures for Hierarchical Zero-shot Reinforcement Learning

Hierarchical reinforcement learning can improve generalization by decomposing long-horizon decision-making into simpler subproblems. However, existing approaches often rely on restrictive design choices, such as fixed temporal abstractions or goal-conditioned objectives, which largely confine them to goal-reaching tasks and limit their applicability to general reward functions. In this paper, we introduce switching successor measures, an extension of successor measures that enables hierarchical control in zero-shot reinforcement learning without additional supervision, fixed horizons, or manually designed subgoals. We show that switching successor measures arise naturally from classical successor measures while preserving their underlying structure. Building on this result, we propose FB $π$-Switch, an algorithm that extracts both a high-level subgoal-selection policy and a low-level control policy directly from forward-backward (FB) representations, allowing hierarchical behavior to emerge from a single learned representation. Experiments on both goal-conditioned and general reward-based tasks show that FB $π$-Switch improves over non-hierarchical baselines and matches state-of-the-art hierarchical methods in goal-conditioned settings. These results demonstrate that structured successor representations provide a flexible foundation for hierarchical zero-shot reinforcement learning beyond goal-reaching tasks. Our project website is available at: https://stestokth.github.io/switching-successors/.

preprint2022arXiv

Best Policy Identification in Linear MDPs

We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of samples required to identify an $\varepsilon$-optimal policy with probability $1-δ$. The lower bound characterizes the optimal sampling rule as the solution of an intricate non-convex optimization program, but can be used as the starting point to devise simple and near-optimal sampling rules and algorithms. We devise such algorithms. One of these exhibits a sample complexity upper bounded by ${\cal O}({\frac{d}{(\varepsilon+Δ)^2}} (\log(\frac{1}δ)+d))$ where $Δ$ denotes the minimum reward gap of sub-optimal actions and $d$ is the dimension of the feature space. This upper bound holds in the moderate-confidence regime (i.e., for all $δ$), and matches existing minimax and gap-dependent lower bounds. We extend our algorithm to episodic linear MDPs.

preprint2022arXiv

Learning Optimal Antenna Tilt Control Policies: A Contextual Linear Bandit Approach

Controlling antenna tilts in cellular networks is imperative to reach an efficient trade-off between network coverage and capacity. In this paper, we devise algorithms learning optimal tilt control policies from existing data (in the so-called passive learning setting) or from data actively generated by the algorithms (the active learning setting). We formalize the design of such algorithms as a Best Policy Identification (BPI) problem in Contextual Linear Multi-Arm Bandits (CL-MAB). An arm represents an antenna tilt update; the context captures current network conditions; the reward corresponds to an improvement of performance, mixing coverage and capacity; and the objective is to identify, with a given level of confidence, an approximately optimal policy (a function mapping the context to an arm with maximal reward). For CL-MAB in both active and passive learning settings, we derive information-theoretical lower bounds on the number of samples required by any algorithm returning an approximately optimal policy with a given level of certainty, and devise algorithms achieving these fundamental limits. We apply our algorithms to the Remote Electrical Tilt (RET) optimization problem in cellular networks, and show that they can produce optimal tilt update policy using much fewer data samples than naive or existing rule-based learning algorithms.

preprint2022arXiv

Measurement-based Admission Control in Sliced Networks: A Best Arm Identification Approach

In sliced networks, the shared tenancy of slices requires adaptive admission control of data flows, based on measurements of network resources. In this paper, we investigate the design of measurement-based admission control schemes, deciding whether a new data flow can be admitted and in this case, on which slice. The objective is to devise a joint measurement and decision strategy that returns a correct decision (e.g., the least loaded slice) with a certain level of confidence while minimizing the measurement cost (the number of measurements made before committing to the decision). We study the design of such strategies for several natural admission criteria specifying what a correct decision is. For each of these criteria, using tools from best arm identification in bandits, we first derive an explicit information-theoretical lower bound on the cost of any algorithm returning the correct decision with fixed confidence. We then devise a joint measurement and decision strategy achieving this theoretical limit. We compare empirically the measurement costs of these strategies, and compare them both to the lower bounds as well as a naive measurement scheme. We find that our algorithm significantly outperforms the naive scheme (by a factor $2-8$).

preprint2021arXiv

Distributed Algorithms that Solve Boolean Equations with Local and Differential Privacies

In this paper, we propose distributed algorithms that solve a system of Boolean equations over a network, where each node in the network possesses only one Boolean equation from the system. The Boolean equation assigned at any particular node is a {\em private} equation known to this node only, and the nodes aim to compute the exact set of solutions to the system without exchanging their local equations. We show that each private Boolean equation can be locally lifted to a linear algebraic equation under a basis of Boolean vectors, leading to a network linear equation that is distributedly solvable using existing distributed linear equation algorithms as a subroutine. A number of exact or approximate solutions to the induced linear equation are then computed at each node from different initial values. The solutions to the original Boolean equations are eventually computed locally via a Boolean vector search algorithm. We prove that given solvable Boolean equations, when the initial values of the nodes for the distributed linear equation solving step are i.i.d selected according to a uniform distribution in a high-dimensional cube, our algorithms return the exact solution set of the Boolean equations at each node with high probability. Furthermore, we present an algorithm for distributed verification of the satisfiability of Boolean equations, and prove its correctness. Finally, we show that by utilizing linear equation solvers with differential privacy to replace the in-network computing routines, the overall distributed Boolean equation algorithms can be made differentially private. Under the standard Laplace mechanism, we prove an explicit level of noises that can be injected in the linear equation steps for ensuring a prescribed level of differential privacy.

preprint2020arXiv

Finite-time Identification of Stable Linear Systems: Optimality of the Least-Squares Estimator

We present a new finite-time analysis of the estimation error of the Ordinary Least Squares (OLS) estimator for stable linear time-invariant systems. We characterize the number of observed samples (the length of the observed trajectory) sufficient for the OLS estimator to be $(\varepsilon,δ)$-PAC, i.e., to yield an estimation error less than $\varepsilon$ with probability at least $1-δ$. We show that this number matches existing sample complexity lower bounds [1,2] up to universal multiplicative factors (independent of ($\varepsilon,δ)$ and of the system). This paper hence establishes the optimality of the OLS estimator for stable systems, a result conjectured in [1]. Our analysis of the performance of the OLS estimator is simpler, sharper, and easier to interpret than existing analyses. It relies on new concentration results for the covariates matrix.

preprint2020arXiv

Off-policy Learning for Remote Electrical Tilt Optimization

We address the problem of Remote Electrical Tilt (RET) optimization using off-policy Contextual Multi-Armed-Bandit (CMAB) techniques. The goal in RET optimization is to control the orientation of the vertical tilt angle of the antenna to optimize Key Performance Indicators (KPIs) representing the Quality of Service (QoS) perceived by the users in cellular networks. Learning an improved tilt update policy is hard. On the one hand, coming up with a new policy in an online manner in a real network requires exploring tilt updates that have never been used before, and is operationally too risky. On the other hand, devising this policy via simulations suffers from the simulation-to-reality gap. In this paper, we circumvent these issues by learning an improved policy in an offline manner using existing data collected on real networks. We formulate the problem of devising such a policy using the off-policy CMAB framework. We propose CMAB learning algorithms to extract optimal tilt update policies from the data. We train and evaluate these policies on real-world 4G Long Term Evolution (LTE) cellular network data. Our policies show consistent improvements over the rule-based logging policy used to collect the data.

preprint2020arXiv

Optimal Best-arm Identification in Linear Bandits

We study the problem of best-arm identification with fixed confidence in stochastic linear bandits. The objective is to identify the best arm with a given level of certainty while minimizing the sampling budget. We devise a simple algorithm whose sampling complexity matches known instance-specific lower bounds, asymptotically almost surely and in expectation. The algorithm relies on an arm sampling rule that tracks an optimal proportion of arm draws, and that remarkably can be updated as rarely as we wish, without compromising its theoretical guarantees. Moreover, unlike existing best-arm identification strategies, our algorithm uses a stopping rule that does not depend on the number of arms. Experimental results suggest that our algorithm significantly outperforms existing algorithms. The paper further provides a first analysis of the best-arm identification problem in linear bandits with a continuous set of arms.

preprint2020arXiv

Predictive Bandits

We introduce and study a new class of stochastic bandit problems, referred to as predictive bandits. In each round, the decision maker first decides whether to gather information about the rewards of particular arms (so that their rewards in this round can be predicted). These measurements are costly, and may be corrupted by noise. The decision maker then selects an arm to be actually played in the round. Predictive bandits find applications in many areas; e.g. they can be applied to channel selection problems in radio communication systems. In this paper, we provide the first theoretical results about predictive bandits, and focus on scenarios where the decision maker is allowed to measure at most one arm per round. We derive asymptotic instance-specific regret lower bounds for these problems, and develop algorithms whose regret match these fundamental limits. We illustrate the performance of our algorithms through numerical experiments. In particular, we highlight the gains that can be achieved by using reward predictions, and investigate the impact of the noise in the corresponding measurements.