# Distributional Method for Risk Averse Reinforcement Learning

## TL;DR

This paper presents a distributional reinforcement learning approach for risk-averse policies in Markov decision processes, leveraging neural networks to efficiently handle randomized policies and avoid the curse of dimensionality.

## Contribution

It introduces a novel distributional method for risk-averse reinforcement learning that effectively incorporates randomized policies and exploits problem structure to mitigate dimensionality issues.

## Key findings

- The proposed method successfully avoids the curse of dimensionality.
- Neural network approximation effectively models the value distribution.
- The approach performs well across various randomly chosen model parameters.

## Abstract

We introduce a distributional method for learning the optimal policy in risk averse Markov decision process with finite state action spaces, latent costs, and stationary dynamics. We assume sequential observations of states, actions, and costs and assess the performance of a policy using dynamic risk measures constructed from nested Kusuoka-type conditional risk mappings. For such performance criteria, randomized policies may outperform deterministic policies, therefore, the candidate policies lie in the d-dimensional simplex where d is the cardinality of the action space. Existing risk averse reinforcement learning methods seldom concern randomized policies, na\"ive extensions to current setting suffer from the curse of dimensionality. By exploiting certain structures embedded in the corresponding dynamic programming principle, we propose a distributional learning method for seeking the optimal policy. The conditional distribution of the value function is casted into a specific type of function, which is chosen with in mind the ease of risk averse optimization. We use a deep neural network to approximate said function, illustrate that the proposed method avoids the curse of dimensionality in the exploration phase, and explore the method's performance with a wide range of model parameters that are picked randomly.