تقرير
Risk-sensitive Markov Decision Process and Learning under General Utility Functions
| العنوان: | Risk-sensitive Markov Decision Process and Learning under General Utility Functions |
|---|---|
| المؤلفون: | Wu, Zhengqi, Xu, Renyuan |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Machine Learning, Mathematics - Optimization and Control |
| الوصف: | 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. For both algorithms, we match the theoretical lower bounds for the risk-neutral setting. Comment: 36 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.13589 |
| رقم الأكسشن: | edsarx.2311.13589 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |