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In recent years significant progress has been made in dealing with challenging problems using reinforcement learning.Despite its great success, reinforcement learning still faces challenge in continuous control tasks. Conventional methods…
Recursion is the fundamental paradigm to finitely describe potentially infinite objects. As state-of-the-art reinforcement learning (RL) algorithms cannot directly reason about recursion, they must rely on the practitioner's ingenuity in…
Unlike their conventional use as estimators of probability density functions in reinforcement learning (RL), this paper introduces a novel function-approximation role for Gaussian mixture models (GMMs) as direct surrogates for Q-function…
Offline reinforcement learning (RL) aims to learn an effective policy from a static dataset. To alleviate extrapolation errors, existing studies often uniformly regularize the value function or policy updates across all states. However, due…
Off-Policy Evaluation (OPE) serves as one of the cornerstones in Reinforcement Learning (RL). Fitted Q Evaluation (FQE) with various function approximators, especially deep neural networks, has gained practical success. While statistical…
Model-free algorithms for reinforcement learning typically require a condition called Bellman completeness in order to successfully operate off-policy with function approximation, unless additional conditions are met. However, Bellman…
Model-free reinforcement learning (RL) algorithms, such as Q-learning, directly parameterize and update value functions or policies without explicitly modeling the environment. They are typically simpler, more flexible to use, and thus more…
We study reinforcement learning (RL) for a class of continuous-time linear-quadratic (LQ) control problems for diffusions, where states are scalar-valued and running control rewards are absent but volatilities of the state processes depend…
Deep reinforcement learning has achieved impressive successes yet often requires a very large amount of interaction data. This result is perhaps unsurprising, as using complicated function approximation often requires more data to fit, and…
The linear Markov Decision Process (MDP) framework offers a principled foundation for reinforcement learning (RL) with strong theoretical guarantees and sample efficiency. However, its restrictive assumption-that both transition dynamics…
While Bayesian-based exploration often demonstrates superior empirical performance compared to bonus-based methods in model-based reinforcement learning (RL), its theoretical understanding remains limited for model-free settings. Existing…
This paper studies the robustness of reinforcement learning algorithms to errors in the learning process. Specifically, we revisit the benchmark problem of discrete-time linear quadratic regulation (LQR) and study the long-standing open…
In offline reinforcement learning (RL) we have no opportunity to explore so we must make assumptions that the data is sufficient to guide picking a good policy, taking the form of assuming some coverage, realizability, Bellman completeness,…
With the increasing need for handling large state and action spaces, general function approximation has become a key technique in reinforcement learning (RL). In this paper, we propose a general framework that unifies model-based and…
Off-policy evaluation (OPE) is a fundamental task in reinforcement learning (RL). In the classic setting of linear OPE, finite-sample guarantees often take the form $$ \textrm{Evaluation error} \le \textrm{poly}(C^\pi, d,…
Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a…
The curse of dimensionality is a widely known issue in reinforcement learning (RL). In the tabular setting where the state space $\mathcal{S}$ and the action space $\mathcal{A}$ are both finite, to obtain a nearly optimal policy with…
Entropy regularized algorithms such as Soft Q-learning and Soft Actor-Critic, recently showed state-of-the-art performance on a number of challenging reinforcement learning (RL) tasks. The regularized formulation modifies the standard RL…
Reinforcement Learning (RL) remains a central optimisation framework in machine learning. Although RL agents can converge to optimal solutions, the definition of ``optimality'' depends on the environment's statistical properties. The…
We consider online reinforcement learning (RL) in episodic Markov decision processes (MDPs) under the linear $q^\pi$-realizability assumption, where it is assumed that the action-values of all policies can be expressed as linear functions…