Related papers: On the solution of stochastic optimization and var…
Chance constrained optimization problems allow to model problems where constraints involving stochastic components should only be violated with a small probability. Evolutionary algorithms have been applied to this scenario and shown to…
Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for…
We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…
When the nonconvex problem is complicated by stochasticity, the sample complexity of stochastic first-order methods may depend linearly on the problem dimension, which is undesirable for large-scale problems. To alleviate this linear…
In this paper we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following…
We consider the problem of asynchronous stochastic optimization, where an optimization algorithm makes updates based on stale stochastic gradients of the objective that are subject to an arbitrary (possibly adversarial) sequence of delays.…
The last decade witnessed a rise in the importance of supervised learning applications involving {\em big data} and {\em big models}. Big data refers to situations where the amounts of training data available and needed causes difficulties…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
A general class of nonconvex optimization problems is considered, where the penalty is the composition of a linear operator with a nonsmooth nonconvex mapping, which is concave on the positive real line. The necessary optimality condition…
Evolutionary strategies have recently been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. In such problems, one often needs to optimize an objective function subject to a set of…
Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…
In the past few decades, many multiobjective evolutionary optimization algorithms (MOEAs) have been proposed to find a finite set of approximate Pareto solutions for a given problem in a single run, each with its own structure. However, in…
We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…
We consider the misspecified optimization problem of minimizing a convex function $f(x;\theta^*)$ in $x$ over a conic constraint set represented by $h(x;\theta^*) \in \mathcal{K}$, where $\theta^*$ is an unknown (or misspecified) vector of…
We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the…
We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can…
Classical theory for quasi-Newton schemes has focused on smooth deterministic unconstrained optimization while recent forays into stochastic convex optimization have largely resided in smooth, unconstrained, and strongly convex regimes.…
For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…