Policy Gradients for CVaR-Constrained MDPs
This work addresses risk-sensitive decision-making in reinforcement learning for applications like finance or robotics, but it is incremental as it builds on existing CVaR estimation and policy gradient methods.
The paper tackles the problem of finding risk-optimal policies in stochastic shortest path problems with Conditional Value-at-Risk constraints, proposing two algorithms that combine stochastic approximation, mini-batches, policy gradients, and importance sampling, and establishing their asymptotic convergence.
We study a risk-constrained version of the stochastic shortest path (SSP) problem, where the risk measure considered is Conditional Value-at-Risk (CVaR). We propose two algorithms that obtain a locally risk-optimal policy by employing four tools: stochastic approximation, mini batches, policy gradients and importance sampling. Both the algorithms incorporate a CVaR estimation procedure, along the lines of Bardou et al. [2009], which in turn is based on Rockafellar-Uryasev's representation for CVaR and utilize the likelihood ratio principle for estimating the gradient of the sum of one cost function (objective of the SSP) and the gradient of the CVaR of the sum of another cost function (in the constraint of SSP). The algorithms differ in the manner in which they approximate the CVaR estimates/necessary gradients - the first algorithm uses stochastic approximation, while the second employ mini-batches in the spirit of Monte Carlo methods. We establish asymptotic convergence of both the algorithms. Further, since estimating CVaR is related to rare-event simulation, we incorporate an importance sampling based variance reduction scheme into our proposed algorithms.