Estimate Sequences for Stochastic Composite Optimization: Variance Reduction, Acceleration, and Robustness to Noise

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of stochastic optimization methods as procedures that iteratively minimize a surrogate of the objective, which covers the stochastic gradient descent method and variants of the incremental approaches SAGA, SVRG, and MISO/Finito/SDCA. This point of view has several advantages: (i) we provide a simple generic proof of convergence for all of the aforementioned methods; (ii) we naturally obtain new algorithms with the same guarantees; (iii) we derive generic strategies to make these algorithms robust to stochastic noise, which is useful when data is corrupted by small random perturbations. Finally, we propose a new accelerated stochastic gradient descent algorithm and an accelerated SVRG algorithm with optimal complexity that is robust to stochastic noise.Comment: Journal of Machine Learning Research, Microtome Publishing, In pres

Optimality and robustness in path-planning under initial uncertainty

Classical deterministic optimal control problems assume full information about the controlled process. The theory of control for general partially-observable processes is powerful, but the methods are computationally expensive and typically address the problems with stochastic dynamics and continuous (directly unobserved) stochastic perturbations. In this paper we focus on path planning problems which are in between -- deterministic, but with an initial uncertainty on either the target or the running cost on parts of the domain. That uncertainty is later removed at some time $T$, and the goal is to choose the optimal trajectory until then. We address this challenge for three different models of information acquisition: with fixed $T$, discretely distributed and exponentially distributed random $T$. We develop models and numerical methods suitable for multiple notions of optimality: based on the average-case performance, the worst-case performance, the average constrained by the worst, the average performance with probabilistic constraints on the bad outcomes, risk-sensitivity, and distributional-robustness. We illustrate our approach using examples of pursuing random targets identified at a (possibly random) later time $T$.Comment: 24 pages, 14 figures. Keywords: optimal control, path-planning, Hamilton-Jacobi PDEs, uncertainty, robustness, delayed information acquisitio

Dual control variate for faster black-box variational inference

Black-box variational inference is a widely-used framework for Bayesian posterior inference, but in some cases suffers from high variance in gradient estimates, harming accuracy and efficiency. This variance comes from two sources of randomness: Data subsampling and Monte Carlo sampling. Whereas existing control variates only address Monte Carlo noise and incremental gradient methods typically only address data subsampling, we propose a new "dual" control variate capable of jointly reducing variance from both sources of noise. We confirm that this leads to reduced variance and improved optimization in several real-world applications

A Latency-driven Availability Assessment for Multi-Tenant Service Chains

Nowadays, most telecommunication services adhere to the Service Function Chain (SFC) paradigm, where network functions are implemented via software. In particular, container virtualization is becoming a popular approach to deploy network functions and to enable resource slicing among several tenants. The resulting infrastructure is a complex system composed by a huge amount of containers implementing different SFC functionalities, along with different tenants sharing the same chain. The complexity of such a scenario lead us to evaluate two critical metrics: the steady-state availability (the probability that a system is functioning in long runs) and the latency (the time between a service request and the pertinent response). Consequently, we propose a latency-driven availability assessment for multi-tenant service chains implemented via Containerized Network Functions (CNFs). We adopt a multi-state system to model single CNFs and the queueing formalism to characterize the service latency. To efficiently compute the availability, we develop a modified version of the Multidimensional Universal Generating Function (MUGF) technique. Finally, we solve an optimization problem to minimize the SFC cost under an availability constraint. As a relevant example of SFC, we consider a containerized version of IP Multimedia Subsystem, whose parameters have been estimated through fault injection techniques and load tests

Fourth NASA Workshop on Computational Control of Flexible Aerospace Systems, part 1

The proceedings of the workshop are presented. Some areas of discussion are as follows: modeling, systems identification, and control of flexible aircraft, spacecraft, and robotic systems