Related papers: A Stochastic Derivative-Free Optimization Method w…
A core principle in statistical learning is that smoothness of target functions allows to break the curse of dimensionality. However, learning a smooth function seems to require enough samples close to one another to get meaningful estimate…
In this paper, we propose a new method based on the Sliding Algorithm from Lan(2016, 2019) for the convex composite optimization problem that includes two terms: smooth one and non-smooth one. Our method uses the stochastic noised…
We study stochastic zeroth-order optimization with decision-dependent distributions, where the sampling law depends on the current decision and only noisy function values are available. For the non-smooth non-convex setting, we establish an…
Accurate simulation of complex physical systems enables the development, testing, and certification of control strategies before they are deployed into the real systems. As simulators become more advanced, the analytical tractability of the…
We investigate in this paper an alternative method to simulation based recursive importance sampling procedure to estimate the optimal change of measure for Monte Carlo simulations. We propose an algorithm which combines (vector and…
To train accurate deep object detectors under the extreme foreground-background imbalance, heuristic sampling methods are always necessary, which either re-sample a subset of all training samples (hard sampling methods, \eg biased sampling,…
Robust controllers that stabilize dynamical systems even under disturbances and noise are often formulated as solutions of nonsmooth, nonconvex optimization problems. While methods such as gradient sampling can handle the nonconvexity and…
We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…
Recent policy optimization approaches (Schulman et al., 2015a; 2017) have achieved substantial empirical successes by constructing new proxy optimization objectives. These proxy objectives allow stable and low variance policy learning, but…
We consider stochastic zero-order optimization problems, which arise in settings from simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic…
Optimization algorithms appear in the core calculations of numerous Artificial Intelligence (AI) and Machine Learning methods, as well as Engineering and Business applications. Following recent works on the theoretical deficiencies of AI, a…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
We propose a novel zeroth-order optimization algorithm based on an efficient sampling strategy. Under mild global regularity conditions on the objective function, we establish non-asymptotic convergence rates for the proposed method.…
In this paper, we study a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term. While restart strategies…
We introduce a theoretical and practical framework for efficient importance sampling of mini-batch samples for gradient estimation from single and multiple probability distributions. To handle noisy gradients, our framework dynamically…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
We consider the problem of sampling from a target distribution, which is \emph {not necessarily logconcave}, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017). Non-asymptotic…
The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…
We present two easy-to-implement gradient-free/zeroth-order methods to optimize a stochastic non-smooth function accessible only via a black-box. The methods are built upon efficient first-order methods in the heavy-tailed case, i.e., when…