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Bayesian Optimization aims at optimizing an unknown non-convex/concave function that is costly to evaluate. We are interested in application scenarios where concurrent function evaluations are possible. Under such a setting, BO could choose…

In this article, variational state estimation is examined from the dynamic programming perspective. This leads to two different value functional recursions depending on whether backward or forward dynamic programming is employed. The result…

We consider the sequential decision-making problem where the mean outcome is a non-linear function of the chosen action. Compared with the linear model, two curious phenomena arise in non-linear models: first, in addition to the "learning…

The Markov Decision Process (MDP) is a popular framework for sequential decision-making problems, and uncertainty quantification is an essential component of it to learn optimal decision-making strategies. In particular, a Bayesian…

Bayesian Optimization is the state of the art technique for the optimization of black boxes, i.e., functions where we do not have access to their analytical expression nor its gradients, they are expensive to evaluate and its evaluation is…

Expected Improvement (EI) is arguably the most popular acquisition function in Bayesian optimization and has found countless successful applications, but its performance is often exceeded by that of more recent methods. Notably, EI and its…

Increased access to computing resources has led to the development of algorithms that can run efficiently on multi-core processing units or in distributed computing environments. In the context of Bayesian inference, many parallel computing…

This note re-visits the rolling-horizon control approach to the problem of a Markov decision process (MDP) with infinite-horizon discounted expected reward criterion. Distinguished from the classical value-iteration approach, we develop an…

Financial markets are complex environments that produce enormous amounts of noisy and non-stationary data. One fundamental problem is online portfolio selection, the goal of which is to exploit this data to sequentially select portfolios of…

In this paper, we deal with batch Bayesian Optimization (Bayes-Opt) problems over a box and we propose a novel bi-objective optimization (BOO) acquisition strategy to sample points where to evaluate the objective function. The BOO problem…

Reinforcement learning (RL) is a fundamental framework for sequential decision-making, in which an agent learns an optimal policy through interactions with an unknown environment. In settings with function approximation, many existing RL…

We study revenue optimization in a repeated auction between a single seller and a single buyer. Traditionally, the design of repeated auctions requires strong modeling assumptions about the bidder behavior, such as it being myopic, infinite…

In this paper, we describe a two-stage method for solving optimization problems with bound constraints. It combines the active-set estimate described in [Facchinei and Lucidi, 1995] with a modification of the non-monotone line search…

This paper studies a long-term resource allocation problem over multiple periods where each period requires a multi-stage decision-making process. We formulate the problem as an online allocation problem in an episodic finite-horizon…

Active learning provides a framework to adaptively query the most informative experiments towards learning an unknown black-box function. Various approaches of active learning have been proposed in the literature, however, they either focus…

This paper proposes a primal-dual framework to learn a stable estimator for linear constrained estimation problems leveraging the moving horizon approach. To avoid the online computational burden in most existing methods, we learn a…

Infinite horizon optimal stopping problems for a L\'evy processes with a two-sided reward function are considered. A two-sided verification theorem is presented in terms of the overall supremum and the overall infimum of the process. A…

We consider bi-objective ranking and selection problems, where the goal is to correctly identify the Pareto optimal solutions among a finite set of candidates for which the two objective outcomes have been observed with uncertainty (e.g.,…

The input to the stochastic orienteering problem consists of a budget $B$ and metric $(V,d)$ where each vertex $v$ has a job with deterministic reward and random processing time (drawn from a known distribution). The processing times are…

Bayesian optimal experimental design has immense potential to inform the collection of data so as to subsequently enhance our understanding of a variety of processes. However, a major impediment is the difficulty in evaluating optimal…