Finite Sample Analysis of Mean-Volatility Actor-Critic for Risk-Averse Reinforcement Learning
Khaled Eldowa, Lorenzo Bisi, Marcello Restelli
Abstract
The goal in the standard reinforcement learning problem is to find a policy that optimizes the expected return. However, such an objective is not adequate in a lot of real-life applications, like finance, where controlling the uncertainty of the outcome is imperative. The mean-volatility objective penalizes, through a tunable parameter, policies with high variance of the per-step reward. An interesting property of this objective is that it admits simple linear Bellman equations that resemble, up to a reward transformation, those of the risk-neutral case. However, the required reward transformation is policy-dependent, and requires the (usually unknown) expected return of the used policy. In this work, we propose two general methods for policy evaluation under the mean-volatility objective: the direct method and the factored method. We then extend recent results for finite sample analysis in the risk-neutral actor-critic setting to the mean-volatility case. Our analysis shows that the sample complexity to attain an $\epsilon$-accurate stationary point is the same as that of the risk-neutral version, using either policy evaluation method for training the critic. Finally, we carry out experiments to test the proposed methods in a simple environment that exhibits some trade-off between optimality, in expectation, and uncertainty of outcome.
BibTeX
@InProceedings{pmlr-v151-eldowa22a,
title = { Finite Sample Analysis of Mean-Volatility Actor-Critic for Risk-Averse Reinforcement Learning },
author = {Eldowa, Khaled and Bisi, Lorenzo and Restelli, Marcello},
booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
pages = {10028--10066},
year = {2022},
editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel},
volume = {151},
series = {Proceedings of Machine Learning Research},
month = {28--30 Mar},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v151/eldowa22a/eldowa22a.pdf},
url = {https://proceedings.mlr.press/v151/eldowa22a.html},
abstract = { The goal in the standard reinforcement learning problem is to find a policy that optimizes the expected return. However, such an objective is not adequate in a lot of real-life applications, like finance, where controlling the uncertainty of the outcome is imperative. The mean-volatility objective penalizes, through a tunable parameter, policies with high variance of the per-step reward. An interesting property of this objective is that it admits simple linear Bellman equations that resemble, up to a reward transformation, those of the risk-neutral case. However, the required reward transformation is policy-dependent, and requires the (usually unknown) expected return of the used policy. In this work, we propose two general methods for policy evaluation under the mean-volatility objective: the direct method and the factored method. We then extend recent results for finite sample analysis in the risk-neutral actor-critic setting to the mean-volatility case. Our analysis shows that the sample complexity to attain an $\epsilon$-accurate stationary point is the same as that of the risk-neutral version, using either policy evaluation method for training the critic. Finally, we carry out experiments to test the proposed methods in a simple environment that exhibits some trade-off between optimality, in expectation, and uncertainty of outcome. }
}