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We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark…

Machine Learning · Computer Science 2013-02-12 H. Brendan McMahan

Simple Stochastic Games (SSGs) were introduced by Anne Condon in 1990, as the simplest version of Stochastic Games for which there is no known polynomial-time algorithm. Condon showed that Stochastic Games are polynomial-time reducible to…

Computational Complexity · Computer Science 2024-02-06 Avi Rudich , Isaac Rudich , Rachel Rue

Worst-case hardness results for most equilibrium computation problems have raised the need for beyond-worst-case analysis. To this end, we study the smoothed complexity of finding pure Nash equilibria in Network Coordination Games, a…

Computational Complexity · Computer Science 2019-02-27 Shant Boodaghians , Rucha Kulkarni , Ruta Mehta

We study a generalized binary search problem on the line and general trees. On the line (e.g., a sorted array), binary search finds a target node in $O(\log n)$ queries in the worst case, where $n$ is the number of nodes. In situations with…

Data Structures and Algorithms · Computer Science 2024-06-19 Agustín Caracci , Christoph Dürr , José Verschae

We present a randomized polynomial-time simplex algorithm with higher probability and tighter bounds for linear programming by applying improved quasi-convex properties, a logarithmic rounding on a given polytope and its logarithmic…

Computational Complexity · Computer Science 2026-05-01 Daniel Gibor

In this paper we provide an $\tilde{O}(nd+d^{3})$ time randomized algorithm for solving linear programs with $d$ variables and $n$ constraints with high probability. To obtain this result we provide a robust, primal-dual…

Data Structures and Algorithms · Computer Science 2021-08-24 Jan van den Brand , Yin Tat Lee , Aaron Sidford , Zhao Song

In this paper, we describe randomized Shellsort--a simple, randomized, data-oblivious version of the Shellsort algorithm that always runs in O(n log n) time and, as we show, succeeds in sorting any given input permutation with very high…

Data Structures and Algorithms · Computer Science 2015-03-13 Michael T. Goodrich

We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small…

Data Structures and Algorithms · Computer Science 2009-09-25 Daniel A. Spielman , Shang-Hua Teng

The classical algorithm for solving B\"uchi games requires time $O(n\cdot m)$ for game graphs with $n$ states and $m$ edges. For game graphs with constant outdegree, the best known algorithm has running time $O(n^2/\log n)$. We present two…

Computer Science and Game Theory · Computer Science 2008-12-18 Krishnendu Chatterjee , Thomas A. Henzinger , Nir Piterman

One-clock priced timed games is a class of two-player, zero-sum, continuous-time games that was defined and thoroughly studied in previous works. We show that one-clock priced timed games can be solved in time m 12^n n^(O(1)), where n is…

Computer Science and Game Theory · Computer Science 2013-01-15 Thomas Dueholm Hansen , Rasmus Ibsen-Jensen , Peter Bro Miltersen

Box-simplex games are a family of bilinear minimax objectives which encapsulate graph-structured problems such as maximum flow [She17], optimal transport [JST19], and bipartite matching [AJJ+22]. We develop efficient near-linear time,…

Data Structures and Algorithms · Computer Science 2022-06-15 Arun Jambulapati , Yujia Jin , Aaron Sidford , Kevin Tian

We present fast and efficient randomized distributed algorithms to find Hamiltonian cycles in random graphs. In particular, we present a randomized distributed algorithm for the $G(n,p)$ random graph model, with number of nodes $n$ and…

Data Structures and Algorithms · Computer Science 2018-04-25 Soumyottam Chatterjee , Reza Fathi , Gopal Pandurangan , Nguyen Dinh Pham

Simple stochastic games can be solved by value iteration (VI), which yields a sequence of under-approximations of the value of the game. This sequence is guaranteed to converge to the value only in the limit. Since no stopping criterion is…

Logic in Computer Science · Computer Science 2021-02-02 Edon Kelmendi , Julia Krämer , Jan Kretinsky , Maximilian Weininger

We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…

Optimization and Control · Mathematics 2021-08-30 James Renegar , Song Zhou

The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…

Combinatorics · Mathematics 2020-06-05 Pu Gao , Bogumil Kaminski , Calum MacRury , Pawel Pralat

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…

Machine Learning · Computer Science 2015-03-19 Alexander Rakhlin , Ohad Shamir , Karthik Sridharan

The area of sublinear algorithms have recently received a lot of attention. In this setting, one has to choose specific access model for the input, as the algorithm does not have time to pre-process or even to see the whole input. A…

Data Structures and Algorithms · Computer Science 2020-09-24 Jakub Tětek

This paper concerns {\em randomized} leader election in synchronous distributed networks. A distributed leader election algorithm is presented for complete $n$-node networks that runs in O(1) rounds and (with high probability) uses only…

Data Structures and Algorithms · Computer Science 2013-05-16 Shay Kutten , Gopal Pandurangan , David Peleg , Peter Robinson , Amitabh Trehan

It is known that greedy methods perform well for maximizing monotone submodular functions. At the same time, such methods perform poorly in the face of non-monotonicity. In this paper, we show - arguably, surprisingly - that invoking the…

Machine Learning · Computer Science 2017-04-07 Moran Feldman , Christopher Harshaw , Amin Karbasi

Advances in generative modeling and adversarial learning have given rise to renewed interest in smooth games. However, the absence of symmetry in the matrix of second derivatives poses challenges that are not present in the classical…

Optimization and Control · Mathematics 2020-10-06 Carles Domingo-Enrich , Fabian Pedregosa , Damien Scieur