Related papers: Pure Exploration with Infinite Answers
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
Unsatisfiable core analysis can boost the computation of optimum stable models for logic programs with weak constraints. However, current solvers employing unsatisfiable core analysis either run to completion, or provide no suboptimal…
The chase procedure is a fundamental algorithmic tool in databases that allows us to reason with constraints, such as existential rules, with a plethora of applications. It takes as input a database and a set of constraints, and iteratively…
A recent body of work addresses safety constraints in explore-and-exploit systems. Such constraints arise where, for example, exploration is carried out by individuals whose welfare should be balanced with overall welfare. In this paper, we…
We return to the subject of stability of infinite time asymptotics of kinetic equations. We found a model which is simpler than those studied previously and which shows unstable behavior corresponding to our arguments to appear elsewhere,…
An interesting open conjecture asks whether it is possible to walk to infinity along primes, where each term in the sequence has one digit more than the previous. We present different greedy models for prime walks to predict the long-time…
In recent years, significant progress has been made on algorithms for learning optimal decision trees, primarily in the context of binary features. Extending these methods to continuous features remains substantially more challenging due to…
We study sparsity in the max-plus algebraic setting. We seek both exact and approximate solutions of the max-plus linear equation with minimum cardinality of support. In the former case, the sparsest solution problem is shown to be…
This paper proposes a finitely terminating algorithm to solve reach-and-stay control problems for nonlinear systems. The algorithm is guaranteed to return a control strategy if the specification is robustly realizable. Such a feature is…
In the literature on optimal stopping, the problem of maximizing the expected discounted reward over all stopping times has been explicitly solved for some special reward functions (including $(x^+)^{\nu}$, $(e^x-K)^+$, $(K-e^{-x})^+$,…
A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE…
It is well-known that for infinitely repeated games, there are computable strategies that have best responses, but no computable best responses. These results were originally proved for either specific games (e.g., Prisoner's dilemma), or…
Most work on adaptive data analysis assumes that samples in the dataset are independent. When correlations are allowed, even the non-adaptive setting can become intractable, unless some structural constraints are imposed. To address this,…
We study pure exploration in bandits, where the dimension of the feature representation can be much larger than the number of arms. To overcome the curse of dimensionality, we propose to adaptively embed the feature representation of each…
Solutions to optimal control problems can be discontinuous, even if all the functionals defining the problem are smooth. This can cause difficulties when numerically computing solutions to these problems. While conventional numerical…
This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed…
We consider a discrete-time bipartite matching model with random arrivals of units of supply and demand that can wait in queues located at the nodes in the network. A control policy determines which are matched at each time. The focus is on…
How to best exploit patchy resources? This long-standing question belongs to the extensively studied class of explore/exploit problems that arise in a wide range of situations, from animal foraging, to robotic exploration, and to human…
We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that…
We study the sequence alignment problem and its independent version, the discrete Hammersley process with an exploration penalty. We obtain rigorous upper bounds for the number of optimality regions in both models near the soft edge. At…