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This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
A popular approach to minimize a finite-sum of convex functions is stochastic gradient descent (SGD) and its variants. Fundamental research questions associated with SGD include: (i) To find a lower bound on the number of times that the…
In this work, solution of the finite horizon hybrid optimal control problem as the central element of the receding horizon optimal control (model predictive control) is investigated based on the indirect approach. The response of a hybrid…
Stochastic gradient descent (SGD) is the workhorse of modern machine learning. Sometimes, there are many different potential gradient estimators that can be used. When so, choosing the one with the best tradeoff between cost and variance is…
Gradient-type distributed optimization methods have blossomed into one of the most important tools for solving a minimization learning task over a networked agent system. However, only one gradient update per iteration is difficult to…
A method is introduced for approximate marginal likelihood inference via adaptive Gaussian quadrature in mixed models with a single grouping factor. The core technical contribution is an algorithm for computing the exact gradient of the…
It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…
In this work, we formulate the problem of achieving in minimum-time perfect chiral resolution with bounded control fields, as an optimal control problem on two non-interacting spins-$1/2$. We assume the same control bound for the two Raman…
We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…
We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…
In min-min optimization or max-min optimization, one has to compute the gradient of a function defined as a minimum. In most cases, the minimum has no closed-form, and an approximation is obtained via an iterative algorithm. There are two…
Proximal gradient methods are popular in sparse optimization as they are straightforward to implement. Nevertheless, they achieve biased solutions, requiring many iterations to converge. This work addresses these issues through a suitable…
Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
A novel approach is given to overcome the computational challenges of the full-matrix Adaptive Gradient algorithm (Full AdaGrad) in stochastic optimization. By developing a recursive method that estimates the inverse of the square root of…
We consider pulses of finite duration for coherent control in the presence of classical noise. We derive the corrections to ideal, instantaneous pulses for the case of general decoherence (spin-spin relaxation and spin-lattice relaxation)…
This paper proposes a distributed algorithm for a network of agents to solve an optimization problem with separable objective function and locally coupled constraints. Our strategy is based on reformulating the original constrained problem…
We propose an algorithm to calculate the exact solution for utility optimization problems on finite state spaces under a class of non-differentiable preferences. We prove that optimal strategies must lie on a discrete grid in the plane, and…
Penalty methods are a well known class of algorithms for constrained optimization. They transform a constrained problem into a sequence of unconstrained \emph{penalized} problems in the hope that approximate solutions of the latter converge…