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Quadratic assignment problems are a fundamental class of combinatorial optimization problems which are ubiquitous in applications, yet their exact resolution is NP-hard. To circumvent this impasse, it was proposed to regularize such…
Recent work on approximate linear programming (ALP) techniques for first-order Markov Decision Processes (FOMDPs) represents the value function linearly w.r.t. a set of first-order basis functions and uses linear programming techniques to…
Evaluating performance across optimization algorithms on many problems presents a complex challenge due to the diversity of numerical scales involved. Traditional data processing methods, such as hypothesis testing and Bayesian inference,…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…
Choosing decision variables deterministically (deterministic decision-making) can be regarded as a particular case of choosing decision variables probabilistically (probabilistic decision-making). It is necessary to investigate whether…
Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical…
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…
We introduce an efficient computational framework for solving a class of multi-marginal martingale optimal transport problems, which includes many robust pricing problems of large financial interest. Such problems are typically…
The paper addresses the problem of computing maximal expected time to termination of probabilistic timed automata (PTA) models, under the condition that the system will, eventually, terminate. This problem can exhibit high computational…
The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that…
We study the relationship between the competitive ratio and the tail distribution of randomized online minimization problems. To this end, we define a broad class of online problems that includes some of the well-studied problems like…
We examine the computational complexity of testing and finding small plans in probabilistic planning domains with succinct representations. We find that many problems of interest are complete for a variety of complexity classes: NP, co-NP,…
We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…
This paper shows that it is possible to reason about the safety and termination of programs handling potentially cyclic, singly-linked lists using propositional reasoning even when the safety invariants and termination arguments depend on…
Constrained partially observable Markov decision processes (CPOMDPs) have been used to model various real-world phenomena. However, they are notoriously difficult to solve to optimality, and there exist only a few approximation methods for…
Linear complementarity problems are a powerful tool for modeling many practically relevant situations such as market equilibria. They also connect many sub-areas of mathematics like game theory, optimization, and matrix theory. Despite…
We formulate pure characteristics demand models under uncertainties of probability distributions as distributionally robust mathematical programs with stochastic complementarity constraints (DRMP-SCC). For any fixed first-stage variable and…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
We analyze an optimal stopping problem with a series of inequality-type and equality-type expectation constraints in a general non-Markovian framework. We show that the optimal stopping problem with expectation constraints (OSEC) in an…
A recurring pattern in "reasoning without training" is that base LLMs already assign non-trivial probability mass to correct multi-step solutions; the bottleneck is locating these modes efficiently at inference time. Power sampling provides…