Related papers: An Exponential Lower Bound for Zadeh's pivot rule

The existence of a pivot rule for the simplex method that guarantees a strongly polynomial run-time is a longstanding, fundamental open problem in the theory of linear programming. The leading pivot rule in theory is the shadow pivot rule,…

The behavior of the simplex algorithm is a widely studied subject. Specifically, the question of the existence of a polynomial pivot rule for the simplex algorithm is of major importance. Here, we give exponential lower bounds for three…

In 2011, Friedmann [F 7] claimed to have proved that pathological linear programs existed for which the Simplex method using Zadeh's least-entered rule [Z 14] would take an exponential number of pivots. In 2019, Disser and Hopp [DH 5]…

We investigate the worst-case behavior of the simplex algorithm on linear programs with three variables, that is, on 3-dimensional simple polytopes. Among the pivot rules that we consider, the ``random edge'' rule yields the best asymptotic…

In this paper we give an exponential lower bound for Cunningham's least recently considered (round-robin) rule as applied to parity games, Markhov decision processes and linear programs. This improves a recent subexponential bound of…

The existence of a polynomial pivot rule for the simplex method for linear programming, policy iteration for Markov decision processes, and strategy improvement for parity games each are prominent open problems in their respective fields.…

This paper presents a new exponential lower bound for the two most popular deterministic variants of the strategy improvement algorithms for solving parity, mean payoff, discounted payoff and simple stochastic games. The first variant…

We construct a family of Markov decision processes for which the policy iteration algorithm needs an exponential number of improving switches with Dantzig's rule, with Bland's rule, and with the Largest Increase pivot rule. This immediately…

We study policy iteration for infinite-horizon Markov decision processes. It has recently been shown policy iteration style algorithms have exponential lower bounds in a two player game setting. We extend these lower bounds to Markov…

The Random-Facet algorithm of Kalai and of Matousek, Sharir and Welzl is an elegant randomized algorithm for solving linear programs and more general LP-type problems. Its expected subexponential time of $2^{\tilde{O}(\sqrt{m})}$, where $m$…

We show subexponential lower bounds (i.e., $2^{\Omega (n^c)}$) on the smoothed complexity of the classical Howard's Policy Iteration algorithm for Markov Decision Processes. The bounds hold for the total reward and the average reward…

Opacity is a property of privacy and security applications asking whether, given a system model, a passive intruder that makes online observations of system's behaviour can ascertain some "secret" information of the system. Deciding opacity…

We prove a tight lower bound (up to constant factors) on the sample complexity of any non-interactive local differentially private protocol for optimizing a linear function over the simplex. This lower bound also implies a tight lower bound…

This paper presents a new lower bound for the discrete strategy improvement algorithm for solving parity games due to Voege and Jurdziski. First, we informally show which structures are difficult to solve for the algorithm. Second, we…

In Friedmann, Hansen, and Zwick (2011) we claimed that the expected number of pivoting steps performed by the Random-Facet algorithm of Kalai and of Matousek, Sharir, and Welzl is equal to the expected number of pivoting steps performed by…

We study the running time, in terms of first order oracle queries, of differentially private empirical/population risk minimization of Lipschitz convex losses. We first consider the setting where the loss is non-smooth and the optimizer…

This paper discusses a data-driven, empirically-based framework to make algorithmic decisions or recommendations without expert knowledge. We improve the performance of two algorithmic case studies: the selection of a pivot rule for the…

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…

We prove that the simplex method with the highest gain/most-negative-reduced cost pivoting rule converges in strongly polynomial time for deterministic Markov decision processes (MDPs) regardless of the discount factor. For a deterministic…

The existence of a polynomial-time pivot rule for the simplex method is a fundamental open question in optimization. While many super-polynomial lower bounds exist for individual or very restricted classes of pivot rules, there currently is…