Chance constrained safe reinforcement learning improves rare risk control
Learning Chance-Constrained MDPs with Bellman Distributional Certificates
Machine Learning
Summary
Safe reinforcement learning usually tries to limit average risks but can miss rare dangerous outcomes. The authors study chance-constrained decision processes, which set strict limits on how likely bad events are. They develop new mathematical tools called Bellman distributional certificates that help plan and learn safe policies more efficiently, even with many possible options. Their approach is tested both in simple examples and a power grid storage task, showing it better manages rare risks safely.
What this means in practice
- •For energy grid operators: Manage energy storage safely under uncertainty by limiting chance of rare high-cost events in control decisions.
- •For autonomous vehicle engineers: Design controllers that strictly limit probability of rare but costly safety violations in uncertain environments.
Authors
Chenbei Lu, Hongyu Yi
Abstract
Safe reinforcement learning (RL) commonly enforces expected-cost constraints, but such expectation safety may fail to control the probability of rare high-cost trajectories. Chance-constrained MDPs (CCMDPs) impose a stronger probability-level requirement, but are widely viewed as harder because the chance constraint is nonconvex and depends on the full trajectory rather than a Bellman-linear expectation. In this paper, we reveal that this computational difficulty does not necessarily imply a higher statistical price. For tabular discounted CCMDPs with fixed bounded successor support and access to a certified planning oracle, we establish a model-based upper bound, with a matching lower bound up to logarithmic terms. Technically, our key idea is the \emph{Bellman distributional certificate}, which constructs a Bellman recursion for constraint violation probabilities before policy selection. The certificate can be reused across candidate policies; combined with shared row-wise reverse-KL confidence sets, it gives a policy-uniform trajectory-KL transfer without a union bound over policies or time--budget Bellman tables. For stochastic policies, we give a model-free variance-reduced policy-gradient algorithm with a finite-sample expected KKT-residual guarantee and independent validation of every accepted policy. Numerical experiments on synthetic CCMDPs and an IEEE 14-bus energy storage control benchmark illustrate the safety and mechanism behavior of the proposed algorithms.