arXiv subjects

Marnix Suilen

Publications and source records attributed to Marnix Suilen.

15 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↗

arXiv2026

On the Complexity of Robust Markov Decision Processes and Bisimulation Metrics

Robust Markov decision processes (RMDPs) extend standard Markov decision processes (MDPs) to account for uncertainty in the transition probabilities. RMDPs have an uncertainty set that defines a set of possible transition functions, each of which induces a standard MDP. The natural objective in an RMDP is to optimize the discounted cumulative reward under the worst-case transition function in the uncertainty set. We study the complexity of the associated threshold problem for RMDPs with polytopic uncertainty sets in halfspace representation. Previous results focused on approximating the optimum or restricted attention to specific subclasses of RMDPs, such as interval MDPs or $L_\infty$-RMDPs. Our contributions are threefold: (1) For (s,a)-rectangular RMDPs, we prove that robust policy evaluation is in P via robust linear programming, and that the threshold problem is in NP. As a corollary, robust policy iteration is a polynomial-time algorithm for these RMDPs when the discount factor is fixed. (2) For $s$-rectangular RMDPs, we show that the threshold problem is in PSPACE via the first-order theory of the reals. (3) We establish lower bounds by reducing both parity games and bisimulation metrics between MDP states to the RMDP threshold problem. A polynomial-time algorithm for the threshold problem would resolve the long-standing open question of whether parity games can be solved in polynomial time. The reduction from bisimulation metrics also yields a practical benefit: it allows us to apply robust policy iteration as a more efficient alternative to the standard fixed-point iteration, as our empirical evaluation demonstrates.

cs.LO↗

arXiv2025

Multi-Environment POMDPs: Discrete Model Uncertainty Under Partial Observability

Multi-environment POMDPs (ME-POMDPs) extend standard POMDPs with discrete model uncertainty. ME-POMDPs represent a finite set of POMDPs that share the same state, action, and observation spaces, but may arbitrarily vary in their transition, observation, and reward models. Such models arise, for instance, when multiple domain experts disagree on how to model a problem. The goal is to find a single policy that is robust against any choice of POMDP within the set, i.e., a policy that maximizes the worst-case reward across all POMDPs. We generalize and expand on existing work in the following way. First, we show that ME-POMDPs can be generalized to POMDPs with sets of initial beliefs, which we call adversarial-belief POMDPs (AB-POMDPs). Second, we show that any arbitrary ME-POMDP can be reduced to a ME-POMDP that only varies in its transition and reward functions or only in its observation and reward functions, while preserving (optimal) policies. We then devise exact and approximate (point-based) algorithms to compute robust policies for AB-POMDPs, and thus ME-POMDPs. We demonstrate that we can compute policies for standard POMDP benchmarks extended to the multi-environment setting.

cs.AI↗

arXiv2025

Pessimistic Iterative Planning with RNNs for Robust POMDPs

Robust POMDPs extend classical POMDPs to incorporate model uncertainty using so-called uncertainty sets on the transition and observation functions, effectively defining ranges of probabilities. Policies for robust POMDPs must be (1) memory-based to account for partial observability and (2) robust against model uncertainty to account for the worst-case probability instances from the uncertainty sets. To compute such robust memory-based policies, we propose the pessimistic iterative planning (PIP) framework, which alternates between (1) selecting pessimistic POMDPs via worst-case probability instances from the uncertainty sets, and (2) computing finite-state controllers (FSCs) for these pessimistic POMDPs. Within PIP, we propose the rFSCNet algorithm, which optimizes a recurrent neural network to compute the FSCs. The empirical evaluation shows that rFSCNet can compute better-performing robust policies than several baselines and a state-of-the-art robust POMDP solver.

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↗

arXiv2024

Robust Markov Decision Processes: A Place Where AI and Formal Methods Meet

Markov decision processes (MDPs) are a standard model for sequential decision-making problems and are widely used across many scientific areas, including formal methods and artificial intelligence (AI). MDPs do, however, come with the restrictive assumption that the transition probabilities need to be precisely known. Robust MDPs (RMDPs) overcome this assumption by instead defining the transition probabilities to belong to some uncertainty set. We present a gentle survey on RMDPs, providing a tutorial covering their fundamentals. In particular, we discuss RMDP semantics and how to solve them by extending standard MDP methods such as value iteration and policy iteration. We also discuss how RMDPs relate to other models and how they are used in several contexts, including reinforcement learning and abstraction techniques. We conclude with some challenges for future work on RMDPs.

cs.AI↗

arXiv2024

Imprecise Probabilities Meet Partial Observability: Game Semantics for Robust POMDPs

Partially observable Markov decision processes (POMDPs) rely on the key assumption that probability distributions are precisely known. Robust POMDPs (RPOMDPs) alleviate this concern by defining imprecise probabilities, referred to as uncertainty sets. While robust MDPs have been studied extensively, work on RPOMDPs is limited and primarily focuses on algorithmic solution methods. We expand the theoretical understanding of RPOMDPs by showing that 1) different assumptions on the uncertainty sets affect optimal policies and values; 2) RPOMDPs have a partially observable stochastic game (POSG) semantic; and 3) the same RPOMDP with different assumptions leads to semantically different POSGs and, thus, different policies and values. These novel semantics for RPOMDPs give access to results for POSGs, studied in game theory; concretely, we show the existence of a Nash equilibrium. Finally, we classify the existing RPOMDP literature using our semantics, clarifying under which uncertainty assumptions these existing works operate.

cs.AI↗

arXiv2024

A PSPACE Algorithm for Almost-Sure Rabin Objectives in Multi-Environment MDPs

Markov Decision Processes (MDPs) model systems with uncertain transition dynamics. Multiple-environment MDPs (MEMDPs) extend MDPs. They intuitively reflect finite sets of MDPs that share the same state and action spaces but differ in the transition dynamics. The key objective in MEMDPs is to find a single policy that satisfies a given objective in every associated MDP. The main result of this paper is PSPACE-completeness for almost-sure Rabin objectives in MEMDPs. This result clarifies the complexity landscape for MEMDPs and contrasts with results for the more general class of partially observable MDPs (POMDPs), where almost-sure reachability is already EXPTIME-complete, and almost-sure Rabin objectives are undecidable.

cs.LO↗

arXiv2023

Robust Anytime Learning of Markov Decision Processes

Markov decision processes (MDPs) are formal models commonly used in sequential decision-making. MDPs capture the stochasticity that may arise, for instance, from imprecise actuators via probabilities in the transition function. However, in data-driven applications, deriving precise probabilities from (limited) data introduces statistical errors that may lead to unexpected or undesirable outcomes. Uncertain MDPs (uMDPs) do not require precise probabilities but instead use so-called uncertainty sets in the transitions, accounting for such limited data. Tools from the formal verification community efficiently compute robust policies that provably adhere to formal specifications, like safety constraints, under the worst-case instance in the uncertainty set. We continuously learn the transition probabilities of an MDP in a robust anytime-learning approach that combines a dedicated Bayesian inference scheme with the computation of robust policies. In particular, our method (1) approximates probabilities as intervals, (2) adapts to new data that may be inconsistent with an intermediate model, and (3) may be stopped at any time to compute a robust policy on the uMDP that faithfully captures the data so far. Furthermore, our method is capable of adapting to changes in the environment. We show the effectiveness of our approach and compare it to robust policies computed on uMDPs learned by the UCRL2 reinforcement learning algorithm in an experimental evaluation on several benchmarks.

cs.AI↗

arXiv2023

More for Less: Safe Policy Improvement With Stronger Performance Guarantees

In an offline reinforcement learning setting, the safe policy improvement (SPI) problem aims to improve the performance of a behavior policy according to which sample data has been generated. State-of-the-art approaches to SPI require a high number of samples to provide practical probabilistic guarantees on the improved policy's performance. We present a novel approach to the SPI problem that provides the means to require less data for such guarantees. Specifically, to prove the correctness of these guarantees, we devise implicit transformations on the data set and the underlying environment model that serve as theoretical foundations to derive tighter improvement bounds for SPI. Our empirical evaluation, using the well-established SPI with baseline bootstrapping (SPIBB) algorithm, on standard benchmarks shows that our method indeed significantly reduces the sample complexity of the SPIBB algorithm.

cs.LG↗

arXiv2023

Decision-Making Under Uncertainty: Beyond Probabilities

This position paper reflects on the state-of-the-art in decision-making under uncertainty. A classical assumption is that probabilities can sufficiently capture all uncertainty in a system. In this paper, the focus is on the uncertainty that goes beyond this classical interpretation, particularly by employing a clear distinction between aleatoric and epistemic uncertainty. The paper features an overview of Markov decision processes (MDPs) and extensions to account for partial observability and adversarial behavior. These models sufficiently capture aleatoric uncertainty but fail to account for epistemic uncertainty robustly. Consequently, we present a thorough overview of so-called uncertainty models that exhibit uncertainty in a more robust interpretation. We show several solution techniques for both discrete and continuous models, ranging from formal verification, over control-based abstractions, to reinforcement learning. As an integral part of this paper, we list and discuss several key challenges that arise when dealing with rich types of uncertainty in a model-based fashion.

cs.AI↗

arXiv2023

Safe Policy Improvement for POMDPs via Finite-State Controllers

We study safe policy improvement (SPI) for partially observable Markov decision processes (POMDPs). SPI is an offline reinforcement learning (RL) problem that assumes access to (1) historical data about an environment, and (2) the so-called behavior policy that previously generated this data by interacting with the environment. SPI methods neither require access to a model nor the environment itself, and aim to reliably improve the behavior policy in an offline manner. Existing methods make the strong assumption that the environment is fully observable. In our novel approach to the SPI problem for POMDPs, we assume that a finite-state controller (FSC) represents the behavior policy and that finite memory is sufficient to derive optimal policies. This assumption allows us to map the POMDP to a finite-state fully observable MDP, the history MDP. We estimate this MDP by combining the historical data and the memory of the FSC, and compute an improved policy using an off-the-shelf SPI algorithm. The underlying SPI method constrains the policy-space according to the available data, such that the newly computed policy only differs from the behavior policy when sufficient data was available. We show that this new policy, converted into a new FSC for the (unknown) POMDP, outperforms the behavior policy with high probability. Experimental results on several well-established benchmarks show the applicability of the approach, even in cases where finite memory is not sufficient.

cs.AI↗

arXiv2021

Robust Finite-State Controllers for Uncertain POMDPs

Uncertain partially observable Markov decision processes (uPOMDPs) allow the probabilistic transition and observation functions of standard POMDPs to belong to a so-called uncertainty set. Such uncertainty, referred to as epistemic uncertainty, captures uncountable sets of probability distributions caused by, for instance, a lack of data available. We develop an algorithm to compute finite-memory policies for uPOMDPs that robustly satisfy specifications against any admissible distribution. In general, computing such policies is theoretically and practically intractable. We provide an efficient solution to this problem in four steps. (1) We state the underlying problem as a nonconvex optimization problem with infinitely many constraints. (2) A dedicated dualization scheme yields a dual problem that is still nonconvex but has finitely many constraints. (3) We linearize this dual problem and (4) solve the resulting finite linear program to obtain locally optimal solutions to the original problem. The resulting problem formulation is exponentially smaller than those resulting from existing methods. We demonstrate the applicability of our algorithm using large instances of an aircraft collision-avoidance scenario and a novel spacecraft motion planning case study.

cs.AI↗

arXiv2021

Balancing Wind and Batteries: Towards Predictive Verification of Smart Grids

We study a smart grid with wind power and battery storage. Traditionally, day-ahead planning aims to balance demand and wind power, yet actual wind conditions often deviate from forecasts. Short-term flexibility in storage and generation fills potential gaps, planned on a minutes time scale for 30-60 minute horizons. Finding the optimal flexibility deployment requires solving a semi-infinite non-convex stochastic program, which is generally intractable to do exactly. Previous approaches rely on sampling, yet such critical problems call for rigorous approaches with stronger guarantees. Our method employs probabilistic model checking techniques. First, we cast the problem as a continuous-space Markov decision process with discretized control, for which an optimal deployment strategy minimizes the expected grid frequency deviation. To mitigate state space explosion, we exploit specific structural properties of the model to implement an iterative exploration method that reuses pre-computed values as wind data is updated. Our experiments show the method's feasibility and versatility across grid configurations and time scales.

eess.SY↗

arXiv2020

Robust Policy Synthesis for Uncertain POMDPs via Convex Optimization

We study the problem of policy synthesis for uncertain partially observable Markov decision processes (uPOMDPs). The transition probability function of uPOMDPs is only known to belong to a so-called uncertainty set, for instance in the form of probability intervals. Such a model arises when, for example, an agent operates under information limitation due to imperfect knowledge about the accuracy of its sensors. The goal is to compute a policy for the agent that is robust against all possible probability distributions within the uncertainty set. In particular, we are interested in a policy that robustly ensures the satisfaction of temporal logic and expected reward specifications. We state the underlying optimization problem as a semi-infinite quadratically-constrained quadratic program (QCQP), which has finitely many variables and infinitely many constraints. Since QCQPs are non-convex in general and practically infeasible to solve, we resort to the so-called convex-concave procedure to convexify the QCQP. Even though convex, the resulting optimization problem still has infinitely many constraints and is NP-hard. For uncertainty sets that form convex polytopes, we provide a transformation of the problem to a convex QCQP with finitely many constraints. We demonstrate the feasibility of our approach by means of several case studies that highlight typical bottlenecks for our problem. In particular, we show that we are able to solve benchmarks with hundreds of thousands of states, hundreds of different observations, and we investigate the effect of different levels of uncertainty in the models.

math.OC↗