Related papers: An Adaptive Step Toward the Multiphase Conjecture

This paper considers multiple binary hypothesis tests with adaptive allocation of sensing resources from a shared budget over a small number of stages. A Bayesian formulation is provided for the multistage allocation problem of minimizing…

Modern statistical analyses often involve testing large numbers of hypotheses. In many situations, these hypotheses may have an underlying tree structure that not only helps determine the order that tests should be conducted but also…

We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in polynomial time. The problem is relevant…

A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…

We consider a bilevel attacker-defender problem to find the worst-case attack on the relays that control the transmission grid. The attacker maximizes load shed by infiltrating a number of relays and rendering the components connected to…

In this work, we prove a $\tilde{\Omega}(\lg^{3/2} n )$ unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in $n$-node directed acyclic graphs under edge…

The study of nonconvex minimax games has gained significant momentum in machine learning and decision science communities due to their fundamental connections to adversarial training scenarios. This work develops a primal-dual alternating…

For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…

Submodular function minimization (SFM) and matroid intersection are fundamental discrete optimization problems with applications in many fields. It is well known that both of these can be solved making $\mathrm{poly}(N)$ queries to a…

This article addresses the challenge of adapting data-based models over time. We propose a novel two-fold modelling architecture designed to correct plant-model mismatch caused by two types of uncertainty. Out-of-domain uncertainty arises…

We present an extension of the PatchworkMHD code [1], itself an MHD-capable extension of the Patchwork code [2], for which several algorithms presented here were co-developed. Its purpose is to create a multipatch scheme compatible with…

The conjectured hardness of Boolean matrix-vector multiplication has been used with great success to prove conditional lower bounds for numerous important data structure problems, see Henzinger et al. [STOC'15]. In recent work, Larsen and…

We obtain a lower bound of n^Omega(1) on the k-party randomized communication complexity of the Disjointness function in the `Number on the Forehead' model of multiparty communication when k is a constant. For k=o(loglog n), the bounds…

In recent years it has become popular to study dynamic problems in a sensitivity setting: Instead of allowing for an arbitrary sequence of updates, the sensitivity model only allows to apply batch updates of small size to the original input…

The low-degree polynomial framework has been highly successful in predicting computational versus statistical gaps for high-dimensional problems in average-case analysis and machine learning. This success has led to the low-degree…

This paper tackles the challenging problem of finding global optimal solutions for two-stage stochastic programs with continuous decision variables and nonconvex recourse functions. We introduce a two-phase approach. The first phase…

We consider a multistage framework introduced recently where, given a time horizon t=1,2,...,T, the input is a sequence of instances of a (static) combinatorial optimization problem I_1,I_2,...,I_T, (one for each time step), and the goal is…

We study adaptive network models in which coupling weights evolve on a fast time scale relative to the phase dynamics of the nodes. Using Geometric Singular Perturbation Theory (GSPT), we prove that, although the microscopic system is…

We introduce and study the problem of optimizing arbitrary functions over degree sequences of hypergraphs and multihypergraphs. We show that over multihypergraphs the problem can be solved in polynomial time. For hypergraphs, we show that…

In large-scale applications, such as machine learning, it is desirable to design non-convex optimization algorithms with a high degree of parallelization. In this work, we study the adaptive complexity of finding a stationary point, which…