Related papers: The Optimizer Quotient and the Certification Trile…
Developing an optimal PAC learning algorithm in the realizable setting, where empirical risk minimization (ERM) is suboptimal, was a major open problem in learning theory for decades. The problem was finally resolved by Hanneke a few years…
We investigate the probabilistic feasibility of randomized solutions to two distinct classes of uncertain multi-agent optimization programs. We first assume that only the constraints of the program are affected by uncertainty, while the…
The quantified constraint satisfaction problem $\mathrm{QCSP}(\mathcal{A})$ is the problem to decide whether a positive Horn sentence, involving nothing more than the two quantifiers and conjunction, is true on some fixed structure…
We study the secure stochastic convex optimization problem. A learner aims to learn the optimal point of a convex function through sequentially querying a (stochastic) gradient oracle. In the meantime, there exists an adversary who aims to…
Mechanism-mediated service markets with polymatroidal feasibility admit efficient, dominant-strategy incentive-compatible (DSIC) allocation, but these guarantees implicitly assume truthful execution by the marketplace operator. Modelling…
We solve the satisfiability problem for a three-sorted fragment of set theory (denoted $3LQST_0^R$), which admits a restricted form of quantification over individual and set variables and the finite enumeration operator $\{\text{-},…
The fixed-template constraint satisfaction problem (CSP) can be seen as the problem of deciding whether a given primitive positive first-order sentence is true in a fixed structure (also called model). We study a class of problems that…
In the oracle identification problem, we are given oracle access to an unknown N-bit string x promised to belong to a known set C of size M and our task is to identify x. We present a quantum algorithm for the problem that is optimal in its…
We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal of the decision maker is to maximize their total reward, while at the same time achieving small…
Current research on the \textit{Decompose-Then-Verify} paradigm for evaluating the factuality of long-form text typically treats decomposition and verification in isolation, overlooking their interactions and potential misalignment. We find…
We propose the first general and practical framework to design certifiable algorithms for robust geometric perception in the presence of a large amount of outliers. We investigate the use of a truncated least squares (TLS) cost function,…
Optimization in machine learning typically deals with the minimization of empirical objectives defined by training data. However, the ultimate goal of learning is to minimize the error on future data (test error), for which the training…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
Stabilizer states admit compact classical descriptions, but many downstream tasks still require their full amplitude vectors. Since the output itself has size $2^n$, the main algorithmic question is whether one can materialize an $n$-qubit…
A cofactor representation of an ideal element, that is, a representation in terms of the generators, can be considered as a certificate for ideal membership. Such a representation is typically not unique, and some can be a lot more…
This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming $\mathsf{P} \neq…
Three algorithms are presented that determine the existence of satisfying assignments for 3SAT Boolean satisfiability expressions. One algorithm is presented for determining an instance of a satisfying assignment, where such exists. The…
This paper demonstrates the relativity of Computability and Nondeterministic; the nondeterministic is just Turing's undecidable Decision rather than the Nondeterministic Polynomial time. Based on analysis about TM, UM, DTM, NTM, Turing…
In various applications the search for certificates for certain properties (e.g., stability of dynamical systems, program termination) can be formulated as a quantified constraint solving problem with quantifier prefix exists-forall. In…
We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the…