Risk-sensitive Reinforcement Learning Based on Convex Scoring Functions

TL;DR

This paper introduces a risk-sensitive reinforcement learning framework using convex scoring functions, addressing time-inconsistency with an augmented state space and proposing a convergent Actor-Critic algorithm validated in financial simulations.

Contribution

It develops a novel RL approach for broad risk measures, overcoming time-inconsistency and providing theoretical guarantees without requiring continuous MDPs.

Findings

Effective in financial trading simulations

Handles a wide range of risk measures

Convergent auxiliary variable sampling method

Abstract

We propose a reinforcement learning (RL) framework under a broad class of risk objectives, characterized by convex scoring functions. This class covers many common risk measures, such as variance, Expected Shortfall, entropic Value-at-Risk, and mean-risk utility. To resolve the time-inconsistency issue, we consider an augmented state space and an auxiliary variable and recast the problem as a two-state optimization problem. We propose a customized Actor-Critic algorithm and establish some theoretical approximation guarantees. A key theoretical contribution is that our results do not require the Markov decision process to be continuous. Additionally, we propose an auxiliary variable sampling method inspired by the alternating minimization algorithm, which is convergent under certain conditions. We validate our approach in simulation experiments with a financial application in statistical arbitrage trading, demonstrating the effectiveness of the algorithm.