arXiv subjects

Kasper Engelen

Publications and source records attributed to Kasper Engelen.

4 recordsLinked to original sources

arXiv2026

Adaptive Policy Portfolios for Robust Markov Decision Processes

Robust Markov decision processes optimize one policy against a set of plausible transition functions. This can be conservative when the unknown dynamics are fixed and become partially identifiable after deployment. We study adaptive policy portfolios: finite sets of memoryless randomized policies synthesized offline and paired with a lightweight online selector. Robust regret is a natural measure of portfolio quality: for each plausible environment, it measures the loss of the best portfolio member relative to the policy that would have been optimal had that environment been known. Related regret objectives were studied by Ghavamzadeh et al. (2016) with an emphasis on approximations and relaxations for safe policy improvement. We give a complexity-theoretic account of portfolio certification and synthesis. Certifying a given portfolio is $\forall\mathbb{R}$-complete already for deterministic portfolios in acyclic (s,a)-rectangular RMDPs. Synthesizing a portfolio of unary-bounded size is $\exists\forall\mathbb{R}$-complete for general rational polytopes, even with fixed discount and acyclic dynamics. The single-policy case is already hard, both combinatorially and algebraically. Finally, we present an offline portfolio construction that is amenable to runtime specialization.

cs.AI↗

arXiv2025

Data-Efficient Safe Policy Improvement Using Parametric Structure

Safe policy improvement (SPI) is an offline reinforcement learning problem in which a new policy that reliably outperforms the behavior policy with high confidence needs to be computed using only a dataset and the behavior policy. Markov decision processes (MDPs) are the standard formalism for modeling environments in SPI. In many applications, additional information in the form of parametric dependencies between distributions in the transition dynamics is available. We make SPI more data-efficient by leveraging these dependencies through three contributions: (1) a parametric SPI algorithm that exploits known correlations between distributions to more accurately estimate the transition dynamics using the same amount of data; (2) a preprocessing technique that prunes redundant actions from the environment through a game-based abstraction; and (3) a more advanced preprocessing technique, based on satisfiability modulo theory (SMT) solving, that can identify more actions to prune. Empirical results and an ablation study show that our techniques increase the data efficiency of SPI by multiple orders of magnitude while maintaining the same reliability guarantees.

cs.AI↗

arXiv2025

Analyzing Value Functions of States in Parametric Markov Chains

Parametric Markov chains (pMC) are used to model probabilistic systems with unknown or partially known probabilities. Although (universal) pMC verification for reachability properties is known to be coETR-complete, there have been efforts to approach it using potentially easier-to-check properties such as asking whether the pMC is monotonic in certain parameters. In this paper, we first reduce monotonicity to asking whether the reachability probability from a given state is never less than that of another given state. Recent results for the latter property imply an efficient algorithm to collapse same-value equivalence classes, which in turn preserves verification results and monotonicity. We implement our algorithm to collapse "trivial" equivalence classes in the pMC and show empirical evidence for the following: First, the collapse gives reductions in size for some existing benchmarks and significant reductions on some custom benchmarks; Second, the collapse speeds up existing algorithms to check monotonicity and parameter lifting, and hence can be used as a fast pre-processing step in practice.

cs.LO↗

arXiv2023

Graph-Based Reductions for Parametric and Weighted MDPs

We study the complexity of reductions for weighted reachability in parametric Markov decision processes. That is, we say a state p is never worse than q if for all valuations of the polynomial indeterminates it is the case that the maximal expected weight that can be reached from p is greater than the same value from q. In terms of computational complexity, we establish that determining whether p is never worse than q is coETR-complete. On the positive side, we give a polynomial-time algorithm to compute the equivalence classes of the order we study for Markov chains. Additionally, we describe and implement two inference rules to under-approximate the never-worse relation and empirically show that it can be used as an efficient preprocessing step for the analysis of large Markov decision processes.

cs.LO↗