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This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials of the inputs.…
Approximate counting via correlation decay is the core algorithmic technique used in the sharp delineation of the computational phase transition that arises in the approximation of the partition function of anti-ferromagnetic two-spin…
We give a general existence and convergence result for interacting particle systems on locally finite graphs with possibly unbounded degrees or jump rates. We allow the local state space to be Polish, and the jumps at a site to affect the…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
We consider a stochastic process in which independent identically distributed random matrices are multiplied and where the Lyapunov exponent of the product is positive. We continue multiplying the random matrices as long as the norm,…
Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum…
In the target tracking and its engineering applications, recursive state estimation of the target is of fundamental importance. This paper presents a recursive performance bound for dynamic estimation and filtering problem, in the framework…
Polyak-Ruppert averaging is a widely used technique to achieve the optimal asymptotic variance of stochastic approximation (SA) algorithms, yet its high-probability performance guarantees remain underexplored in general settings. In this…
Solving partially observable Markov decision processes (POMDPs) typically requires reasoning about the values of exponentially many state beliefs. Towards practical performance, state-of-the-art solvers use value bounds to guide this…
We propose, analyze, and test a proximal-gradient method for solving regularized optimization problems with general constraints. The method employs a decomposition strategy to compute trial steps and uses a merit function to determine step…
The families of $f$-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability…
The class $\MIP^*$ of promise problems that can be decided through an interactive proof system with multiple entangled provers provides a complexity-theoretic framework for the exploration of the nonlocal properties of entanglement. Little…
We study the persistence probability for processes with stationary increments. Our results apply to a number of examples: sums of stationary correlated random variables whose scaling limit is fractional Brownian motion, random walks in…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
Building on existing $hp$-adaptive algorithms driven by equilibrated-flux estimators from [ESAIM Math. Model. Numer. Anal. 57 (2023), 329--366] and the references therein, we propose a novel $h$-adaptive algorithm for a fixed polynomial…
This paper describes sufficient conditions for the existence of optimal policies for Partially Observable Markov Decision Processes (POMDPs) with Borel state, observation, and action sets and with the expected total costs. Action sets may…
This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
Recent advances have significantly improved our understanding of the sample complexity of learning in average-reward Markov decision processes (AMDPs) under the generative model. However, much less is known about the constrained…