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Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We propose a single time-scale stochastic…
The problem of mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence from observations of the sequence with a noise and missing observations is…
Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning…
This paper addresses a distributed optimization problem in a communication network where nodes are active sporadically. Each active node applies some learning method to control its action to maximize the global utility function, which is…
Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly,…
We consider a one-dimensional stationary stochastic process $x(\tau)$ of duration $T$. We study the probability density function (PDF) $P(t_{\rm m}|T)$ of the time $t_{\rm m}$ at which $x(\tau)$ reaches its global maximum. By using a path…
Trajectory optimization methods for motion planning attempt to generate trajectories that minimize a suitable objective function. Such methods efficiently find solutions even for high degree-of-freedom robots. However, a globally optimal…
We propose a practical Bayesian optimization method using Gaussian process regression, of which the marginal likelihood is maximized where the number of model selection steps is guided by a pre-defined threshold. Since Bayesian optimization…
A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting…
This manuscript reports a stochastic dynamical scenario whose associated stationary probability density function is exactly a previously proposed one to adjust high-frequency traded volume distributions. This dynamical conjecture,…
A gradient-free deterministic method is developed to solve global optimization problems for Lipschitz continuous functions defined in arbitrary path-wise connected compact sets in Euclidean spaces. The method can be regarded as granular…
We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…
The problem of optimal estimation of linear functionals constructed from the unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with stationary noise is considered. For…
Uncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and a dynamic flow model with uncertain boundary data on networks. We introduce two different ways how to compute the…
Optimization by stochastic gradient descent is an important component of many large-scale machine learning algorithms. A wide variety of such optimization algorithms have been devised; however, it is unclear whether these algorithms are…
Partially observable Markov decision processes (POMDPs) with continuous state and observation spaces have powerful flexibility for representing real-world decision and control problems but are notoriously difficult to solve. Recent online…
In this paper, we analyze the optimal management of local memory systems, using the tools of stationary point processes. We provide a rigorous setting of the problem, building upon recent work, and characterize the optimal causal policy…
Searching large and complex design spaces for a global optimum can be infeasible and unnecessary. A practical alternative is to iteratively refine the neighborhood of an initial design using local optimization methods such as gradient…