相关论文: A Gilmore-Gomory-Type Construction of Integer Prog…

Iverson's APL and its descendants (such as J, K and FISh) are examples of the family of "rank-polymorphic" programming languages. The principal control mechanism of such languages is the general lifting of functions that operate on arrays…

We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discrete-time finite horizon Markov decision processes with…

We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…

This work proposes a framework, embedded within the Performance Estimation framework (PEP), for obtaining worst-case performance guarantees on stochastic first-order methods. Given a first-order method, a function class, and a noise model…

We introduce a general technique to create an extended formulation of a mixed-integer program. We classify the integer variables into blocks, each of which generates a finite set of vector values. The extended formulation is constructed by…

In this paper, stability and sensitivity properties of a class of parametric constrained optimization problem, whose feasible region is defined by a set-valued inclusion, are investigated through the associated optimal value function.…

We introduce an extension of decision problems called resiliency problems. In resiliency problems, the goal is to decide whether an instance remains positive after any (appropriately defined) perturbation has been applied to it. To tackle…

Algorithmic analysis of Markov decision processes (MDP) and stochastic games (SG) in practice relies on value-iteration (VI) algorithms. Since basic VI does not provide guarantees on the precision of the result, variants of VI have been…

Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…

Machine Learning (ML) algorithms have been increasingly applied to problems from several different areas. Despite their growing popularity, their predictive performance is usually affected by the values assigned to their hyperparameters…

A magic value in a program is a constant symbol that is essential for the execution of the program but has no clear explanation for its choice. Learning programs with magic values is difficult for existing program synthesis approaches. To…

Software requirements selection aims to find an optimal subset of the requirements with the highest value while respecting the project constraints. But the value of a requirement may depend on the presence or absence of other requirements…

We study the problem of how to construct a set of policies that can be composed together to solve a collection of reinforcement learning tasks. Each task is a different reward function defined as a linear combination of known features. We…

In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one,…

The intention of this note is two-fold. First, we study integer optimization problems in standard form defined by $A \in\mathbb{Z}^{m\times{}n}$ and present an algorithm to solve such problems in polynomial-time provided that both the…

A common characteristic in integer linear programs (ILPs) is symmetry, allowing variables to be permuted without altering the underlying problem structure. Recently, GNNs have emerged as a promising approach for solving ILPs. However, a…

Geometric programming problems occur frequently in engineering design and management. In multiobjective optimization, the trade-off information between different objective functions is probably the most important piece of information in a…

Building upon the dynamic programming principle for set-valued functions arising from many applications, in this paper we propose a new notion of set-valued PDEs. The key component in the theory is a set-valued It\^{o} formula,…

We describe an approach for exploiting structure in Markov Decision Processes with continuous state variables. At each step of the dynamic programming, the state space is dynamically partitioned into regions where the value function is the…

Interpretability is becoming an active research topic as machine learning (ML) models are more widely used to make critical decisions. Tabular data is one of the most commonly used modes of data in diverse applications such as healthcare…