Risk-sensitive Markov Decision Process and Learning under General Utility Functions

• URL: http://arxiv.org/abs/2311.13589v2
• Date: Sat, 21 Dec 2024 04:11:08 GMT
• Title: Risk-sensitive Markov Decision Process and Learning under General Utility Functions
• Authors: Zhengqi Wu, Renyuan Xu,
• Abstract summary: Reinforcement Learning (RL) has gained substantial attention across diverse application domains and theoretical investigations. We consider a scenario where the decision-maker seeks to optimize a general utility function of the cumulative reward in the framework of a decision process (MDP) We propose a modified value iteration algorithm that employs an epsilon-covering over the space of cumulative reward. In the absence of a simulator, our algorithm, designed with an upper-confidence-bound exploration approach, identifies a near-optimal policy.
• Score: 3.069335774032178
• License:
• Abstract: Reinforcement Learning (RL) has gained substantial attention across diverse application domains and theoretical investigations. Existing literature on RL theory largely focuses on risk-neutral settings where the decision-maker learns to maximize the expected cumulative reward. However, in practical scenarios such as portfolio management and e-commerce recommendations, decision-makers often persist in heterogeneous risk preferences subject to outcome uncertainties, which can not be well-captured by the risk-neural framework. Incorporating these preferences can be approached through utility theory, yet the development of risk-sensitive RL under general utility functions remains an open question for theoretical exploration. In this paper, we consider a scenario where the decision-maker seeks to optimize a general utility function of the cumulative reward in the framework of a Markov decision process (MDP). To facilitate the Dynamic Programming Principle and Bellman equation, we enlarge the state space with an additional dimension that accounts for the cumulative reward. We propose a discretized approximation scheme to the MDP under enlarged state space, which is tractable and key for algorithmic design. We then propose a modified value iteration algorithm that employs an epsilon-covering over the space of cumulative reward. When a simulator is accessible, our algorithm efficiently learns a near-optimal policy with guaranteed sample complexity. In the absence of a simulator, our algorithm, designed with an upper-confidence-bound exploration approach, identifies a near-optimal policy while ensuring a guaranteed regret bound. Finally, we establish a novel theoretical regret lower bound for the risk-sensitive setting, and show that the regret of our algorithm matches this lower bound up to a small polynomial factor

Related papers

• Pessimism Meets Risk: Risk-Sensitive Offline Reinforcement Learning [19.292214425524303]
  We study risk-sensitive reinforcement learning (RL), a crucial field due to its ability to enhance decision-making in scenarios where it is essential to manage uncertainty and minimize potential adverse outcomes. Our work focuses on applying the entropic risk measure to RL problems. We center on the linear Markov Decision Process (MDP) setting, a well-regarded theoretical framework that has yet to be examined from a risk-sensitive standpoint.
  arXiv  Detail & Related papers  (2024-07-10T13:09:52Z)
• Risk-Sensitive RL with Optimized Certainty Equivalents via Reduction to Standard RL [48.1726560631463]
  We study Risk-Sensitive Reinforcement Learning with the Optimized Certainty Equivalent (OCE) risk. We propose two general meta-algorithms via reductions to standard RL. We show that it learns the optimal risk-sensitive policy while prior algorithms provably fail.
  arXiv  Detail & Related papers  (2024-03-10T21:45:12Z)
• Provable Risk-Sensitive Distributional Reinforcement Learning with General Function Approximation [54.61816424792866]
  We introduce a general framework on Risk-Sensitive Distributional Reinforcement Learning (RS-DisRL), with static Lipschitz Risk Measures (LRM) and general function approximation. We design two innovative meta-algorithms: textttRS-DisRL-M, a model-based strategy for model-based function approximation, and textttRS-DisRL-V, a model-free approach for general value function approximation.
  arXiv  Detail & Related papers  (2024-02-28T08:43:18Z)
• 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)
• Multivariate Systemic Risk Measures and Computation by Deep Learning Algorithms [63.03966552670014]
  We discuss the key related theoretical aspects, with a particular focus on the fairness properties of primal optima and associated risk allocations. The algorithms we provide allow for learning primals, optima for the dual representation and corresponding fair risk allocations.
  arXiv  Detail & Related papers  (2023-02-02T22:16:49Z)
• Safe Exploration Incurs Nearly No Additional Sample Complexity for Reward-free RL [43.672794342894946]
  Reward-free reinforcement learning (RF-RL) relies on random action-taking to explore the unknown environment without any reward feedback information. It remains unclear how such safe exploration requirement would affect the corresponding sample complexity in order to achieve the desired optimality of the obtained policy in planning. We propose a unified Safe reWard-frEe ExploraTion (SWEET) framework, and develop algorithms coined Tabular-SWEET and Low-rank-SWEET, respectively.
  arXiv  Detail & Related papers  (2022-06-28T15:00:45Z)
• Policy Gradient Bayesian Robust Optimization for Imitation Learning [49.881386773269746]
  We derive a novel policy gradient-style robust optimization approach, PG-BROIL, to balance expected performance and risk. Results suggest PG-BROIL can produce a family of behaviors ranging from risk-neutral to risk-averse.
  arXiv  Detail & Related papers  (2021-06-11T16:49:15Z)
• On the Convergence and Optimality of Policy Gradient for Markov Coherent Risk [32.97618081988295]
  We present a tight upper bound on the suboptimality of the learned policy, characterizing its dependence on the nonlinearity of the objective and the degree of risk aversion. We propose a practical implementation of PG that uses state distribution reweighting to overcome previous limitations.
  arXiv  Detail & Related papers  (2021-03-04T04:11:09Z)
• Risk-Sensitive Deep RL: Variance-Constrained Actor-Critic Provably Finds Globally Optimal Policy [95.98698822755227]
  We make the first attempt to study risk-sensitive deep reinforcement learning under the average reward setting with the variance risk criteria. We propose an actor-critic algorithm that iteratively and efficiently updates the policy, the Lagrange multiplier, and the Fenchel dual variable.
  arXiv  Detail & Related papers  (2020-12-28T05:02:26Z)

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.