Statistical Analysis of Policy Space Compression Problem

Policy search methods are crucial in reinforcement learning, offering a framework to address continuous state-action and partially observable problems. However, the complexity of exploring vast policy spaces can lead to significant inefficiencies. Reducing the policy space through policy compression emerges as a powerful, reward-free approach to accelerate the learning process. This technique condenses the policy space into a smaller, representative set while maintaining most of the original effectiveness. Our research focuses on determining the necessary sample size to learn this compressed set accurately. We employ R\'enyi divergence to measure the similarity between true and estimated policy distributions, establishing error bounds for good approximations. To simplify the analysis, we employ the $l_1$ norm, determining sample size requirements for both model-based and model-free settings. Finally, we correlate the error bounds from the $l_1$ norm with those from R\'enyi divergence, distinguishing between policies near the vertices and those in the middle of the policy space, to determine the lower and upper bounds for the required sample sizes.

A Retrospective on the Robot Air Hockey Challenge: Benchmarking Robust, Reliable, and Safe Learning Techniques for Real-world Robotics

Machine learning methods have a groundbreaking impact in many application domains, but their application on real robotic platforms is still limited. Despite the many challenges associated with combining machine learning technology with robotics, robot learning remains one of the most promising directions for enhancing the capabilities of robots. When deploying learning-based approaches on real robots, extra effort is required to address the challenges posed by various real-world factors. To investigate the key factors influencing real-world deployment and to encourage original solutions from different researchers, we organized the Robot Air Hockey Challenge at the NeurIPS 2023 conference. We selected the air hockey task as a benchmark, encompassing low-level robotics problems and high-level tactics. Different from other machine learning-centric benchmarks, participants need to tackle practical challenges in robotics, such as the sim-to-real gap, low-level control issues, safety problems, real-time requirements, and the limited availability of real-world data. Furthermore, we focus on a dynamic environment, removing the typical assumption of quasi-static motions of other real-world benchmarks. The competition's results show that solutions combining learning-based approaches with prior knowledge outperform those relying solely on data when real-world deployment is challenging. Our ablation study reveals which real-world factors may be overlooked when building a learning-based solution. The successful real-world air hockey deployment of best-performing agents sets the foundation for future competitions and follow-up research directions.

Local Linearity: the Key for No-regret Reinforcement Learning in Continuous MDPs

Achieving the no-regret property for Reinforcement Learning (RL) problems in continuous state and action-space environments is one of the major open problems in the field. Existing solutions either work under very specific assumptions or achieve bounds that are vacuous in some regimes. Furthermore, many structural assumptions are known to suffer from a provably unavoidable exponential dependence on the time horizon $H$ in the regret, which makes any possible solution unfeasible in practice. In this paper, we identify local linearity as the feature that makes Markov Decision Processes (MDPs) both learnable (sublinear regret) and feasible (regret that is polynomial in $H$). We define a novel MDP representation class, namely Locally Linearizable MDPs, generalizing other representation classes like Linear MDPs and MDPS with low inherent Belmman error. Then, i) we introduce Cinderella, a no-regret algorithm for this general representation class, and ii) we show that all known learnable and feasible MDP families are representable in this class. We first show that all known feasible MDPs belong to a family that we call Mildly Smooth MDPs. Then, we show how any mildly smooth MDP can be represented as a Locally Linearizable MDP by an appropriate choice of representation. This way, Cinderella is shown to achieve state-of-the-art regret bounds for all previously known (and some new) continuous MDPs for which RL is learnable and feasible.

Truncating Trajectories in Monte Carlo Policy Evaluation: an Adaptive Approach

Policy evaluation via Monte Carlo (MC) simulation is at the core of many MC Reinforcement Learning (RL) algorithms (e.g., policy gradient methods). In this context, the designer of the learning system specifies an interaction budget that the agent usually spends by collecting trajectories of fixed length within a simulator. However, is this data collection strategy the best option? To answer this question, in this paper, we propose as a quality index a surrogate of the mean squared error of a return estimator that uses trajectories of different lengths, i.e., \emph{truncated}. Specifically, this surrogate shows the sub-optimality of the fixed-length trajectory schedule. Furthermore, it suggests that adaptive data collection strategies that spend the available budget sequentially can allocate a larger portion of transitions in timesteps in which more accurate sampling is required to reduce the error of the final estimate. Building on these findings, we present an adaptive algorithm called Robust and Iterative Data collection strategy Optimization (RIDO). The main intuition behind RIDO is to split the available interaction budget into mini-batches. At each round, the agent determines the most convenient schedule of trajectories that minimizes an empirical and robust version of the surrogate of the estimator's error. After discussing the theoretical properties of our method, we conclude by assessing its performance across multiple domains. Our results show that RIDO can adapt its trajectory schedule toward timesteps where more sampling is required to increase the quality of the final estimation.

Efficient Learning of POMDPs with Known Observation Model in Average-Reward Setting

Dealing with Partially Observable Markov Decision Processes is notably a challenging task. We face an average-reward infinite-horizon POMDP setting with an unknown transition model, where we assume the knowledge of the observation model. Under this assumption, we propose the Observation-Aware Spectral (OAS) estimation technique, which enables the POMDP parameters to be learned from samples collected using a belief-based policy. Then, we propose the OAS-UCRL algorithm that implicitly balances the exploration-exploitation trade-off following the $\textit{optimism in the face of uncertainty}$ principle. The algorithm runs through episodes of increasing length. For each episode, the optimal belief-based policy of the estimated POMDP interacts with the environment and collects samples that will be used in the next episode by the OAS estimation procedure to compute a new estimate of the POMDP parameters. Given the estimated model, an optimization oracle computes the new optimal policy. We show the consistency of the OAS procedure, and we prove a regret guarantee of order $\mathcal{O}(\sqrt{T \log(T)})$ for the proposed OAS-UCRL algorithm. We compare against the oracle playing the optimal stochastic belief-based policy and show the efficient scaling of our approach with respect to the dimensionality of the state, action, and observation space. We finally conduct numerical simulations to validate and compare the proposed technique with other baseline approaches.

Bridging Rested and Restless Bandits with Graph-Triggering: Rising and Rotting

Rested and Restless Bandits are two well-known bandit settings that are useful to model real-world sequential decision-making problems in which the expected reward of an arm evolves over time due to the actions we perform or due to the nature. In this work, we propose Graph-Triggered Bandits (GTBs), a unifying framework to generalize and extend rested and restless bandits. In this setting, the evolution of the arms' expected rewards is governed by a graph defined over the arms. An edge connecting a pair of arms $(i,j)$ represents the fact that a pull of arm $i$ triggers the evolution of arm $j$, and vice versa. Interestingly, rested and restless bandits are both special cases of our model for some suitable (degenerated) graph. As relevant case studies for this setting, we focus on two specific types of monotonic bandits: rising, where the expected reward of an arm grows as the number of triggers increases, and rotting, where the opposite behavior occurs. For these cases, we study the optimal policies. We provide suitable algorithms for all scenarios and discuss their theoretical guarantees, highlighting the complexity of the learning problem concerning instance-dependent terms that encode specific properties of the underlying graph structure.

State and Action Factorization in Power Grids

The increase of renewable energy generation towards the zero-emission target is making the problem of controlling power grids more and more challenging. The recent series of competitions Learning To Run a Power Network (L2RPN) have encouraged the use of Reinforcement Learning (RL) for the assistance of human dispatchers in operating power grids. All the solutions proposed so far severely restrict the action space and are based on a single agent acting on the entire grid or multiple independent agents acting at the substations level. In this work, we propose a domain-agnostic algorithm that estimates correlations between state and action components entirely based on data. Highly correlated state-action pairs are grouped together to create simpler, possibly independent subproblems that can lead to distinct learning processes with less computational and data requirements. The algorithm is validated on a power grid benchmark obtained with the Grid2Op simulator that has been used throughout the aforementioned competitions, showing that our algorithm is in line with domain-expert analysis. Based on these results, we lay a theoretically-grounded foundation for using distributed reinforcement learning in order to improve the existing solutions.

A Provably Efficient Option-Based Algorithm for both High-Level and Low-Level Learning

Hierarchical Reinforcement Learning (HRL) approaches have shown successful results in solving a large variety of complex, structured, long-horizon problems. Nevertheless, a full theoretical understanding of this empirical evidence is currently missing. In the context of the \emph{option} framework, prior research has devised efficient algorithms for scenarios where options are fixed, and the high-level policy selecting among options only has to be learned. However, the fully realistic scenario in which both the high-level and the low-level policies are learned is surprisingly disregarded from a theoretical perspective. This work makes a step towards the understanding of this latter scenario. Focusing on the finite-horizon problem, we present a meta-algorithm alternating between regret minimization algorithms instanced at different (high and low) temporal abstractions. At the higher level, we treat the problem as a Semi-Markov Decision Process (SMDP), with fixed low-level policies, while at a lower level, inner option policies are learned with a fixed high-level policy. The bounds derived are compared with the lower bound for non-hierarchical finite-horizon problems, allowing to characterize when a hierarchical approach is provably preferable, even without pre-trained options.

The Limits of Pure Exploration in POMDPs: When the Observation Entropy is Enough

The problem of pure exploration in Markov decision processes has been cast as maximizing the entropy over the state distribution induced by the agent's policy, an objective that has been extensively studied. However, little attention has been dedicated to state entropy maximization under partial observability, despite the latter being ubiquitous in applications, e.g., finance and robotics, in which the agent only receives noisy observations of the true state governing the system's dynamics. How can we address state entropy maximization in those domains? In this paper, we study the simple approach of maximizing the entropy over observations in place of true latent states. First, we provide lower and upper bounds to the approximation of the true state entropy that only depends on some properties of the observation function. Then, we show how knowledge of the latter can be exploited to compute a principled regularization of the observation entropy to improve performance. With this work, we provide both a flexible approach to bring advances in state entropy maximization to the POMDP setting and a theoretical characterization of its intrinsic limits.

Interpetable Target-Feature Aggregation for Multi-Task Learning based on Bias-Variance Analysis

Multi-task learning (MTL) is a powerful machine learning paradigm designed to leverage shared knowledge across tasks to improve generalization and performance. Previous works have proposed approaches to MTL that can be divided into feature learning, focused on the identification of a common feature representation, and task clustering, where similar tasks are grouped together. In this paper, we propose an MTL approach at the intersection between task clustering and feature transformation based on a two-phase iterative aggregation of targets and features. First, we propose a bias-variance analysis for regression models with additive Gaussian noise, where we provide a general expression of the asymptotic bias and variance of a task, considering a linear regression trained on aggregated input features and an aggregated target. Then, we exploit this analysis to provide a two-phase MTL algorithm (NonLinCTFA). Firstly, this method partitions the tasks into clusters and aggregates each obtained group of targets with their mean. Then, for each aggregated task, it aggregates subsets of features with their mean in a dimensionality reduction fashion. In both phases, a key aspect is to preserve the interpretability of the reduced targets and features through the aggregation with the mean, which is further motivated by applications to Earth science. Finally, we validate the algorithms on synthetic data, showing the effect of different parameters and real-world datasets, exploring the validity of the proposed methodology on classical datasets, recent baselines, and Earth science applications.