Bayesian Risk-Sensitive Policy Optimization For MDPs With General Loss Functions

• URL: http://arxiv.org/abs/2509.15509v2
• Date: Tue, 30 Sep 2025 19:16:01 GMT
• Title: Bayesian Risk-Sensitive Policy Optimization For MDPs With General Loss Functions
• Authors: Xiaoshuang Wang, Yifan Lin, Enlu Zhou,
• Abstract summary: We consider Markov decision processes (MDPs) with a general loss function and unknown parameters.<n>We take a Bayesian approach to estimate the parameters from data and impose a coherent risk functional on the loss.<n>We propose a policy gradient optimization method, leveraging the dual representation of coherent risk measures.
• Score: 8.16996766356341
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Motivated by many application problems, we consider Markov decision processes (MDPs) with a general loss function and unknown parameters. To mitigate the epistemic uncertainty associated with unknown parameters, we take a Bayesian approach to estimate the parameters from data and impose a coherent risk functional (with respect to the Bayesian posterior distribution) on the loss. Since this formulation usually does not satisfy the interchangeability principle, it does not admit Bellman equations and cannot be solved by approaches based on dynamic programming. Therefore, We propose a policy gradient optimization method, leveraging the dual representation of coherent risk measures and extending the envelope theorem to continuous cases. We then show the stationary analysis of the algorithm with a convergence rate of $\mathcal{O}(T^{-1/2}+r^{-1/2})$, where $T$ is the number of policy gradient iterations and $r$ is the sample size of the gradient estimator. We further extend our algorithm to an episodic setting, and establish the global convergence of the extended algorithm and provide bounds on the number of iterations needed to achieve an error bound $\mathcal{O}(\epsilon)$ in each episode.

Related papers

• Provably Efficient Algorithms for S- and Non-Rectangular Robust MDPs with General Parameterization [85.91302339486673]
  We study robust Markov decision processes (RMDPs) with general policy parameterization under s-rectangular and non-rectangular uncertainty sets.<n>We prove novel Lipschitz and Lipschitz-smoothness properties for general policy parameterizations that extends to infinite state spaces.<n>We design a projected gradient descent algorithm for s-rectangular uncertainty and a Frank-Wolfe algorithm for non-rectangular uncertainty.
  arXiv  Detail & Related papers  (2026-02-11T21:44:20Z)
• Parameter-free Algorithms for the Stochastically Extended Adversarial Model [59.81852138768642]
  Existing approaches for the Extended Adversarial (SEA) model require prior knowledge of problem-specific parameters, such as the diameter of the domain $D$ and the Lipschitz constant of the loss functions $G$.<n>We develop parameter-free methods by leveraging the Optimistic Online Newton Step (OONS) algorithm to eliminate the need for these parameters.
  arXiv  Detail & Related papers  (2025-10-06T10:53:37Z)
• A Finite-Sample Analysis of an Actor-Critic Algorithm for Mean-Variance Optimization in a Discounted MDP [1.0923877073891446]
  We analyze a Temporal Difference (TD) learning algorithm with linear function approximation (LFA) for policy evaluation.<n>We derive finite-sample bounds that hold (i) in the mean-squared sense and (ii) with high probability under tail iterate averaging.<n>These results establish finite-sample theoretical guarantees for risk-sensitive actor-critic methods in reinforcement learning.
  arXiv  Detail & Related papers  (2024-06-12T05:49:53Z)
• Reinforcement Learning for Infinite-Horizon Average-Reward Linear MDPs via Approximation by Discounted-Reward MDPs [16.49229317664822]
  We study the problem of infinite-horizon average-reward reinforcement learning with linear decision processes (MDPs)<n>Our approach approximates the average-reward setting by a discounted discounting factor, then applies an optimistic value iteration.
  arXiv  Detail & Related papers  (2024-05-23T20:58:33Z)
• Sample-Efficient Constrained Reinforcement Learning with General Parameterization [35.22742439337603]
  We consider a constrained Markov Decision Problem (CMDP) where the goal of an agent is to maximize the expected discounted sum of rewards over an infinite horizon. We develop the Primal-Dual Accelerated Natural Policy Gradient (PD-ANPG) algorithm that ensures an $epsilon$ global optimality gap and $epsilon$ constraint violation.
  arXiv  Detail & Related papers  (2024-05-17T08:39:05Z)
• FastPart: Over-Parameterized Stochastic Gradient Descent for Sparse optimisation on Measures [3.377298662011438]
  This paper presents a novel algorithm that leverages Gradient Descent strategies in conjunction with Random Features to augment the scalability of Conic Particle Gradient Descent (CPGD)<n>We provide rigorous mathematical proofs demonstrating the following key findings: $mathrm(i)$ The total variation norms of the solution measures along the descent trajectory remain bounded, ensuring stability and preventing undesirable divergence; $mathrm(ii)$ We establish a global convergence guarantee with a convergence rate of $O(log(K)/sqrtK)$ over $K$, showcasing the efficiency and effectiveness of
  arXiv  Detail & Related papers  (2023-12-10T20:41:43Z)
• Model-Based Epistemic Variance of Values for Risk-Aware Policy Optimization [59.758009422067]
  We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. We propose a new uncertainty Bellman equation (UBE) whose solution converges to the true posterior variance over values. We introduce a general-purpose policy optimization algorithm, Q-Uncertainty Soft Actor-Critic (QU-SAC) that can be applied for either risk-seeking or risk-averse policy optimization.
  arXiv  Detail & Related papers  (2023-12-07T15:55:58Z)
• Bayesian Learning of Optimal Policies in Markov Decision Processes with Countably Infinite State-Space [0.0]
  We study the problem of optimal control of a family of discrete-time countable state-space Markov Decision Processes. We propose an algorithm based on Thompson sampling with dynamically-sized episodes. We show that our algorithm can be applied to develop approximately optimal control algorithms.
  arXiv  Detail & Related papers  (2023-06-05T03:57:16Z)
• First-order Policy Optimization for Robust Markov Decision Process [40.2022466644885]
  We consider the problem of solving robust Markov decision process (MDP) MDP involves a set of discounted, finite state, finite action space MDPs with uncertain transition kernels. For $(mathbfs,mathbfa)$-rectangular uncertainty sets, we establish several structural observations on the robust objective.
  arXiv  Detail & Related papers  (2022-09-21T18:10:28Z)
• Navigating to the Best Policy in Markov Decision Processes [68.8204255655161]
  We investigate the active pure exploration problem in Markov Decision Processes. Agent sequentially selects actions and, from the resulting system trajectory, aims at the best as fast as possible.
  arXiv  Detail & Related papers  (2021-06-05T09:16:28Z)
• Joint Optimization of Multi-Objective Reinforcement Learning with Policy Gradient Based Algorithm [50.50545326342971]
  We formulate the problem of maximizing a non-linear concave function of multiple long-term objectives.<n>A policy-gradient based model-free algorithm is proposed for the problem.<n>The proposed algorithm is shown to achieve convergence to within an $epsilon$ of the global optima.
  arXiv  Detail & Related papers  (2021-05-28T22:20:54Z)
• Large-Scale Methods for Distributionally Robust Optimization [53.98643772533416]
  We prove that our algorithms require a number of evaluations gradient independent of training set size and number of parameters. Experiments on MNIST and ImageNet confirm the theoretical scaling of our algorithms, which are 9--36 times more efficient than full-batch methods.
  arXiv  Detail & Related papers  (2020-10-12T17:41:44Z)
• Private Stochastic Non-Convex Optimization: Adaptive Algorithms and Tighter Generalization Bounds [72.63031036770425]
  We propose differentially private (DP) algorithms for bound non-dimensional optimization. We demonstrate two popular deep learning methods on the empirical advantages over standard gradient methods.
  arXiv  Detail & Related papers  (2020-06-24T06:01:24Z)
• Upper Confidence Primal-Dual Reinforcement Learning for CMDP with Adversarial Loss [145.54544979467872]
  We consider online learning for episodically constrained Markov decision processes (CMDPs) We propose a new emphupper confidence primal-dual algorithm, which only requires the trajectories sampled from the transition model. Our analysis incorporates a new high-probability drift analysis of Lagrange multiplier processes into the celebrated regret analysis of upper confidence reinforcement learning.
  arXiv  Detail & Related papers  (2020-03-02T05:02:23Z)
• Provably Efficient Safe Exploration via Primal-Dual Policy Optimization [105.7510838453122]
  We study the Safe Reinforcement Learning (SRL) problem using the Constrained Markov Decision Process (CMDP) formulation. We present an provably efficient online policy optimization algorithm for CMDP with safe exploration in the function approximation setting.
  arXiv  Detail & Related papers  (2020-03-01T17:47:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.