Anytime-Constrained Reinforcement Learning
This addresses a fundamental challenge in reinforcement learning for safety-critical applications where constraints must be strictly enforced, though it is incremental as it builds on existing cMDP frameworks.
The paper tackles the problem of constrained Markov Decision Processes (cMDPs) with anytime constraints, which require the agent to never violate its budget at any time, and shows that optimal deterministic policies exist with a fixed-parameter tractable reduction to unconstrained MDPs, but also proves that computing approximately optimal policies is NP-hard in general.
We introduce and study constrained Markov Decision Processes (cMDPs) with anytime constraints. An anytime constraint requires the agent to never violate its budget at any point in time, almost surely. Although Markovian policies are no longer sufficient, we show that there exist optimal deterministic policies augmented with cumulative costs. In fact, we present a fixed-parameter tractable reduction from anytime-constrained cMDPs to unconstrained MDPs. Our reduction yields planning and learning algorithms that are time and sample-efficient for tabular cMDPs so long as the precision of the costs is logarithmic in the size of the cMDP. However, we also show that computing non-trivial approximately optimal policies is NP-hard in general. To circumvent this bottleneck, we design provable approximation algorithms that efficiently compute or learn an arbitrarily accurate approximately feasible policy with optimal value so long as the maximum supported cost is bounded by a polynomial in the cMDP or the absolute budget. Given our hardness results, our approximation guarantees are the best possible under worst-case analysis.