optimization problem


Intel debuts Pohoiki Springs, a powerful neuromorphic research system for AI workloads

#artificialintelligence

This morning, Intel announced the general readiness of Pohoiki Springs, a powerful self-contained neuromorphic system that's about the size of five standard servers. The company says the system will be available to members of the Intel Neuromorphic Research Community via the cloud using Intel's Nx SDK and community-contributed software components, giving them a tool to scale up their neuromorphic research and explore ways to accelerate workloads that run slowly on today's conventional architectures. Intel claims Pohoiki Springs, which was announced in July 2019, is similar in neural capacity to the brain of a small mammal, with 768 Loihi chips and 100 million neurons spread across 24 Arria10 FPGA Nahuku expansion boards (containing 32 chips each) that operate at under 500 watts. This is ostensibly a step on the path to supporting larger and more sophisticated neuromorphic workloads. In fact, just this week, Intel demonstrated that the chips can be used to "teach" an AI model to distinguish among 10 different scents.




Learning Reward Machines for Partially Observable Reinforcement Learning

Neural Information Processing Systems

Reward Machines (RMs), originally proposed for specifying problems in Reinforcement Learning (RL), provide a structured, automata-based representation of a reward function that allows an agent to decompose problems into subproblems that can be efficiently learned using off-policy learning. Here we show that RMs can be learned from experience, instead of being specified by the user, and that the resulting problem decomposition can be used to effectively solve partially observable RL problems. We pose the task of learning RMs as a discrete optimization problem where the objective is to find an RM that decomposes the problem into a set of subproblems such that the combination of their optimal memoryless policies is an optimal policy for the original problem. We show the effectiveness of this approach on three partially observable domains, where it significantly outperforms A3C, PPO, and ACER, and discuss its advantages, limitations, and broader potential. Papers published at the Neural Information Processing Systems Conference.


Minimal Variance Sampling in Stochastic Gradient Boosting

Neural Information Processing Systems

Stochastic Gradient Boosting (SGB) is a widely used approach to regularization of boosting models based on decision trees. It was shown that, in many cases, random sampling at each iteration can lead to better generalization performance of the model and can also decrease the learning time. Different sampling approaches were proposed, where probabilities are not uniform, and it is not currently clear which approach is the most effective. In this paper, we formulate the problem of randomization in SGB in terms of optimization of sampling probabilities to maximize the estimation accuracy of split scoring used to train decision trees.This optimization problem has a closed-form nearly optimal solution, and it leads to a new sampling technique, which we call Minimal Variance Sampling (MVS).The method both decreases the number of examples needed for each iteration of boosting and increases the quality of the model significantly as compared to the state-of-the art sampling methods. The superiority of the algorithm was confirmed by introducing MVS as a new default option for subsampling in CatBoost, a gradient boosting library achieving state-of-the-art quality on various machine learning tasks.


Learning to Optimize in Swarms

Neural Information Processing Systems

Learning to optimize has emerged as a powerful framework for various optimization and machine learning tasks. Current such "meta-optimizers" often learn in the space of continuous optimization algorithms that are point-based and uncertainty-unaware. To overcome the limitations, we propose a meta-optimizer that learns in the algorithmic space of both point-based and population-based optimization algorithms. Specifically, we learn and interpret the update formula through a population of LSTMs embedded with sample- and feature-level attentions. Meanwhile, we estimate the posterior directly over the global optimum and use an uncertainty measure to help guide the learning process.


Stochastic Frank-Wolfe for Composite Convex Minimization

Neural Information Processing Systems

A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers are designed for the deterministic setting where problem data is readily available. In this setting, generalized conditional gradient methods (aka Frank-Wolfe-type methods) provide scalable solutions by leveraging the so-called linear minimization oracle instead of the projection onto the semidefinite cone. Most problems in machine learning and modern engineering applications, however, contain some degree of stochasticity. In this work, we propose the first conditional-gradient-type method for solving stochastic optimization problems under affine constraints.


An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Neural Information Processing Systems

We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is closely related to the Polyak-Lojasiewicz and Mangasarian-Fromowitz conditions. In particular, when a first-order solver is used for the inner iterates, we prove that iALM finds a first-order stationary point with $\tilde{\mathcal{O}}(1/\epsilon 3)$ calls to the first-order oracle. These complexity results match the known theoretical results in the literature. We also provide strong numerical evidence on large-scale machine learning problems, including the Burer-Monteiro factorization of semidefinite programs, and a novel nonconvex relaxation of the standard basis pursuit template.


Shadowing Properties of Optimization Algorithms

Neural Information Processing Systems

Ordinary differential equation (ODE) models of gradient-based optimization methods can provide insights into the dynamics of learning and inspire the design of new algorithms. Unfortunately, this thought-provoking perspective is weakened by the fact that, in the worst case, the error between the algorithm steps and its ODE approximation grows exponentially with the number of iterations. In an attempt to encourage the use of continuous-time methods in optimization, we show that, if some additional regularity on the objective is assumed, the ODE representations of Gradient Descent and Heavy-ball do not suffer from the aforementioned problem, once we allow for a small perturbation on the algorithm initial condition. In the dynamical systems literature, this phenomenon is called shadowing. Our analysis relies on the concept of hyperbolicity, as well as on tools from numerical analysis.


Continuous-time Models for Stochastic Optimization Algorithms

Neural Information Processing Systems

We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis as well as tools from stochastic calculus, in order to derive convergence bounds for various types of non-convex functions. Guided by such analysis, we show that the same Lyapunov arguments hold in discrete-time, leading to matching rates. In addition, we use these models and Ito calculus to infer novel insights on the dynamics of SGD, proving that a decreasing learning rate acts as time warping or, equivalently, as landscape stretching. Papers published at the Neural Information Processing Systems Conference.