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This paper presents a wp-style calculus for obtaining bounds on the expected run-time of probabilistic programs. Its application includes determining the (possibly infinite) expected termination time of a probabilistic program and proving…

Logic in Computer Science · Computer Science 2022-02-17 Benjamin Lucien Kaminski , Joost-Pieter Katoen , Christoph Matheja , Federico Olmedo

A long line of works characterizes the sample complexity of regret minimization in sequential decision-making by min-max programs. In the corresponding saddle-point game, the min-player optimizes the sampling distribution against an…

Machine Learning · Computer Science 2024-03-18 Johannes Kirschner , Seyed Alireza Bakhtiari , Kushagra Chandak , Volodymyr Tkachuk , Csaba Szepesvári

Several recent works have proposed instance-dependent upper bounds on the number of episodes needed to identify, with probability $1-\delta$, an $\varepsilon$-optimal policy in finite-horizon tabular Markov Decision Processes (MDPs). These…

Machine Learning · Statistics 2023-11-13 Aymen Al-Marjani , Andrea Tirinzoni , Emilie Kaufmann

Turn-based discounted-sum games are two-player zero-sum games played on finite directed graphs. The vertices of the graph are partitioned between player 1 and player 2. Plays are infinite walks on the graph where the next vertex is decided…

Computer Science and Game Theory · Computer Science 2024-05-21 Ali Asadi , Krishnendu Chatterjee , Raimundo Saona , Jakub Svoboda

This work studies external regret in sequential prediction games with both positive and negative payoffs. External regret measures the difference between the payoff obtained by the forecasting strategy and the payoff of the best action. In…

Statistics Theory · Mathematics 2007-06-13 Nicolo Cesa-Bianchi , Yishay Mansour , Gilles Stoltz

In this short paper, we give an upper bound for the number of different basic feasible solutions generated by the simplex method for linear programming problems having optimal solutions. The bound is polynomial of the number of constraints,…

Optimization and Control · Mathematics 2015-03-17 Tomonari Kitahara , Shinji Mizuno

Policy iteration is a family of algorithms that are used to find an optimal policy for a given Markov Decision Problem (MDP). Simple Policy iteration (SPI) is a type of policy iteration where the strategy is to change the policy at exactly…

Machine Learning · Computer Science 2019-12-02 Sarthak Consul , Bhishma Dedhia , Kumar Ashutosh , Parthasarathi Khirwadkar

We prove that the Random-Edge simplex algorithm requires an expected number of at most 13n/sqrt(d) pivot steps on any simple d-polytope with n vertices. This is the first nontrivial upper bound for general polytopes. We also describe a…

Combinatorics · Mathematics 2008-07-15 Bernd Gärtner , Volker Kaibel

We show a methodology for the computation of the probability of deadline miss for a periodic real-time task scheduled by a resource reservation algorithm. We propose a modelling technique for the system that reduces the computation of such…

Performance · Computer Science 2016-04-28 Luigi Palopoli , Daniele Fontanelli , Luca Abeni , Bernardo Villalba Frías

We propose to classify the power of algorithms by the complexity of the problems that they can be used to solve. Instead of restricting to the problem a particular algorithm was designed to solve explicitly, however, we include problems…

Discrete Mathematics · Computer Science 2014-04-03 Yann Disser , Martin Skutella

We consider a general problem of finding a strategy that minimizes the exponential moment of a given cost function, with an emphasis on its relation to the more common criterion of minimization the expectation of the first moment of the…

Information Theory · Computer Science 2011-03-16 Neri Merhav

Let ${\mathcal D}(n)$ be the maximal determinant for $n \times n$ $\{\pm 1\}$-matrices, and $\mathcal R(n) = {\mathcal D}(n)/n^{n/2}$ be the ratio of ${\mathcal D}(n)$ to the Hadamard upper bound. Using the probabilistic method, we prove…

Combinatorics · Mathematics 2016-11-02 Richard P. Brent , Judy-anne H. Osborn , Warren D. Smith

In performative prediction, a predictive model impacts the distribution that generates future data, a phenomenon that is being ignored in classical supervised learning. In this closed-loop setting, the natural measure of performance named…

Machine Learning · Computer Science 2022-10-24 Yulai Zhao

In the (binary) Distinct Vectors problem we are given a binary matrix A with pairwise different rows and want to select at most k columns such that, restricting the matrix to these columns, all rows are still pairwise different. A result by…

Computational Complexity · Computer Science 2023-06-22 Marcin Pilipczuk , Manuel Sorge

We consider random dynamical systems on manifolds modeled by a skew product which have certain geometric properties and whose measures satisfy quenched decay of correlations at a sufficient rate. We prove that the limiting distribution for…

Dynamical Systems · Mathematics 2019-10-03 Nicolai Haydn , Jerome Rousseau , Fan Yang

In probably approximately correct (PAC) reinforcement learning (RL), an agent is required to identify an $\epsilon$-optimal policy with probability $1-\delta$. While minimax optimal algorithms exist for this problem, its instance-dependent…

Machine Learning · Computer Science 2022-10-25 Andrea Tirinzoni , Aymen Al-Marjani , Emilie Kaufmann

The best algorithm so far for solving Simple Stochastic Games is Ludwig's randomized algorithm which works in expected $2^{O(\sqrt{n})}$ time. We first give a simpler iterative variant of this algorithm, using Bland's rule from the simplex…

Data Structures and Algorithms · Computer Science 2019-01-17 David Auger , Pierre Coucheney , Yann Strozecki

With elementary means, we prove a stronger run time guarantee for the univariate marginal distribution algorithm (UMDA) optimizing the LeadingOnes benchmark function in the desirable regime with low genetic drift. If the population size is…

Neural and Evolutionary Computing · Computer Science 2020-04-13 Benjamin Doerr , Martin Krejca

Follow the regularized leader FTRL is the premier algorithm for online optimization. However, despite decades of research on its convergence in constrained optimization -- and potential games in particular -- its behavior remained hitherto…

Computer Science and Game Theory · Computer Science 2026-02-02 Ioannis Anagnostides , Ioannis Panageas , Nikolas Patris , Tuomas Sandholm

We consider a discrete-time Markov decision process with Borel state and action spaces. The performance criterion is to maximize a total expected {utility determined by unbounded return function. It is shown the existence of optimal…

Probability · Mathematics 2018-10-08 François Dufour , Alexandre Genadot