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This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…
Superoptimization requires the estimation of the best program for a given computational task. In order to deal with large programs, superoptimization techniques perform a stochastic search. This involves proposing a modification of the…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
In this paper we look at a class of random optimization problems. We discuss ways that can help determine typical behavior of their solutions. When the dimensions of the optimization problems are large such an information often can be…
We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
This paper studies the problem of learning an unknown function $f$ from given data about $f$. The learning problem is to give an approximation $\hat f$ to $f$ that predicts the values of $f$ away from the data. There are numerous settings…
The fundamental theorem of statistical learning states that for binary classification problems, any Empirical Risk Minimization (ERM) learning rule has close to optimal sample complexity. In this paper we seek for a generic optimal learner…
Conventional reinforcement learning (RL) methods can successfully solve a wide range of sequential decision problems. However, learning policies that can generalize predictably across multiple tasks in a setting with non-Markovian reward…
An agent's ability to leverage past experience is critical for efficiently solving new tasks. Approximate solutions for new tasks can be obtained from previously derived value functions, as demonstrated by research on transfer learning,…
This paper focuses on managing the cost of deliberation before action. In many problems, the overall quality of the solution reflects costs incurred and resources consumed in deliberation as well as the cost and benefit of execution, when…
We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
Predicting the value of a function $f$ at a new point given its values at old points is an ubiquitous scientific endeavor, somewhat less developed when $f$ produces multiple values that depend on one another, e.g. when it outputs…
We study the optimization of functions with $n>2$ arguments that have a representation as a sum of several functions that have only $2$ of the $n$ arguments each, termed sums of bivariates, on finite domains. The complexity of optimizing…
The shortcomings of maximum likelihood estimation in the context of model-based reinforcement learning have been highlighted by an increasing number of papers. When the model class is misspecified or has a limited representational capacity,…
In this paper, we consider multi-objective reinforcement learning, which arises in many real-world problems with multiple optimization goals. We approach the problem with a max-min framework focusing on fairness among the multiple goals and…
We study stochastic programs where the decision-maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. In this setting, the goal is to find a…
We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions…