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

Consider the problem of minimizing functions that are Lipschitz and strongly convex, but not necessarily differentiable. We prove that after $T$ steps of stochastic gradient descent, the error of the final iterate is $O(\log(T)/T)$ with…

In performative stochastic optimization, decisions can influence the distribution of random parameters, rendering the data-generating process itself decision-dependent. In practice, decision-makers rarely have access to the true…

We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…

We prove lower bounds for higher-order methods in smooth non-convex finite-sum optimization. Our contribution is threefold: We first show that a deterministic algorithm cannot profit from the finite-sum structure of the objective, and that…

In a seminal paper in 2013, Witt showed that the (1+1) Evolutionary Algorithm with standard bit mutation needs time $(1+o(1))n \ln n/p_1$ to find the optimum of any linear function, as long as the probability $p_1$ to flip exactly one bit…

A central problem in parameterized algorithms is to obtain algorithms with running time $f(k)\cdot n^{O(1)}$ such that $f$ is as slow growing function of the parameter $k$ as possible. In particular, a large number of basic parameterized…

We show that a variant of the random-edge pivoting rule results in a strongly polynomial time simplex algorithm for linear programs $\max\{c^Tx \colon Ax\leq b\}$, whose constraint matrix $A$ satisfies a geometric property introduced by…

We consider the problem of decision-making with side information and unbounded loss functions. Inspired by probably approximately correct learning model, we use a slightly different model that incorporates the notion of side information in…

In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…

For the last ten years, almost every theoretical result concerning the expected run time of a randomized search heuristic used drift theory, making it the arguably most important tool in this domain. Its success is due to its ease of use…

The celebrated result of Kabanets and Impagliazzo (Computational Complexity, 2004) showed that PIT algorithms imply circuit lower bounds, and vice versa. Since then it has been a major challenge to understand the precise connections between…

A randomized algorithm for a search problem is *pseudodeterministic* if it produces a fixed canonical solution to the search problem with high probability. In their seminal work on the topic, Gat and Goldwasser posed as their main open…

The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…

We consider Incentive Decision Processes, where a principal seeks to reduce its costs due to another agent's behavior, by offering incentives to the agent for alternate behavior. We focus on the case where a principal interacts with a…

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…

A decent number of lower bounds for non-elitist population-based evolutionary algorithms has been shown by now. Most of them are technically demanding due to the (hard to avoid) use of negative drift theorems -- general results which…

The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…

The monotone variational inequality is a central problem in mathematical programming that unifies and generalizes many important settings such as smooth convex optimization, two-player zero-sum games, convex-concave saddle point problems,…

We study the bias of random bounded-degree polynomials over odd prime fields and show that, with probability exponentially close to 1, such polynomials have exponentially small bias. This also yields an exponential tail bound on the weight…

In this paper we consider the problem of obtaining sharp bounds for the performance of temporal difference (TD) methods with linear function approximation for policy evaluation in discounted Markov decision processes. We show that a simple…