Anytime-Constrained Reinforcement Learning

Jeremy McMahan, Xiaojin Zhu
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:4321-4329, 2024.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-mcmahan24a, title = { Anytime-Constrained Reinforcement Learning }, author = {McMahan, Jeremy and Zhu, Xiaojin}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {4321--4329}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/mcmahan24a/mcmahan24a.pdf}, url = {https://proceedings.mlr.press/v238/mcmahan24a.html}, abstract = { 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. } }
Endnote
%0 Conference Paper %T Anytime-Constrained Reinforcement Learning %A Jeremy McMahan %A Xiaojin Zhu %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-mcmahan24a %I PMLR %P 4321--4329 %U https://proceedings.mlr.press/v238/mcmahan24a.html %V 238 %X 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.
APA
McMahan, J. & Zhu, X.. (2024). Anytime-Constrained Reinforcement Learning . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:4321-4329 Available from https://proceedings.mlr.press/v238/mcmahan24a.html.

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