Certifiably Robust Policies for Uncertain Parametric Environments
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arXiv
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| Format: | Preprint |
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2024
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| author | Schnitzer, Yannik Abate, Alessandro Parker, David |
| author_facet | Schnitzer, Yannik Abate, Alessandro Parker, David |
| contents | We present a data-driven approach for producing policies that are provably robust across unknown stochastic environments. Existing approaches can learn models of a single environment as an interval Markov decision processes (IMDP) and produce a robust policy with a probably approximately correct (PAC) guarantee on its performance. However these are unable to reason about the impact of environmental parameters underlying the uncertainty. We propose a framework based on parametric Markov decision processes (MDPs) with unknown distributions over parameters. We learn and analyse IMDPs for a set of unknown sample environments induced by parameters. The key challenge is then to produce meaningful performance guarantees that combine the two layers of uncertainty: (1) multiple environments induced by parameters with an unknown distribution; (2) unknown induced environments which are approximated by IMDPs. We present a novel approach based on scenario optimisation that yields a single PAC guarantee quantifying the risk level for which a specified performance level can be assured in unseen environments, plus a means to trade-off risk and performance. We implement and evaluate our framework using multiple robust policy generation methods on a range of benchmarks. We show that our approach produces tight bounds on a policy's performance with high confidence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_03093 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Certifiably Robust Policies for Uncertain Parametric Environments Schnitzer, Yannik Abate, Alessandro Parker, David Machine Learning Artificial Intelligence Systems and Control We present a data-driven approach for producing policies that are provably robust across unknown stochastic environments. Existing approaches can learn models of a single environment as an interval Markov decision processes (IMDP) and produce a robust policy with a probably approximately correct (PAC) guarantee on its performance. However these are unable to reason about the impact of environmental parameters underlying the uncertainty. We propose a framework based on parametric Markov decision processes (MDPs) with unknown distributions over parameters. We learn and analyse IMDPs for a set of unknown sample environments induced by parameters. The key challenge is then to produce meaningful performance guarantees that combine the two layers of uncertainty: (1) multiple environments induced by parameters with an unknown distribution; (2) unknown induced environments which are approximated by IMDPs. We present a novel approach based on scenario optimisation that yields a single PAC guarantee quantifying the risk level for which a specified performance level can be assured in unseen environments, plus a means to trade-off risk and performance. We implement and evaluate our framework using multiple robust policy generation methods on a range of benchmarks. We show that our approach produces tight bounds on a policy's performance with high confidence. |
| title | Certifiably Robust Policies for Uncertain Parametric Environments |
| topic | Machine Learning Artificial Intelligence Systems and Control |
| url | https://arxiv.org/abs/2408.03093 |