We propose AttendLight, an end-to-end Reinforcement Learning (RL) algorithm for the problem of traffic signal control. Previous approaches for this problem have the shortcoming that they require training for each new intersection with a different structure or traffic flow distribution. AttendLight solves this issue by training a single, universal model for intersections with any number of roads, lanes, phases (possible signals), and traffic flow. To this end, we propose a deep RL model which incorporates two attention models. The first attention model is introduced to handle different numbers of roads-lanes; and the second attention model is intended for enabling decision-making with any number of phases in an intersection. As a result, our proposed model works for any intersection configuration, as long as a similar configuration is represented in the training set. Experiments were conducted with both synthetic and real-world standard benchmark datasets. Our numerical experiment covers intersections with three or four approaching roads; one-directional/bi-directional roads with one, two, and three lanes; different number of phases; and different traffic flows. We consider two regimes: (i) single-environment training, single-deployment, and (ii) multi-environment training, multi-deployment. AttendLight outperforms both classical and other RL-based approaches on all cases in both regimes.

In this paper we consider nonconvex optimization and learning over a network of distributed nodes. We develop a Proximal Primal-Dual Algorithm (Prox-PDA), which enables the network nodes to distributedly and collectively compute the set of first-order stationary solutions in a global sublinear manner [with a rate of $O(1/r)$, where $r$ is the iteration counter]. To the best of our knowledge, this is the first algorithm that enables distributed nonconvex optimization with global rate guarantees. Our numerical experiments also demonstrate the effectiveness of the proposed algorithm.

The nonnegative matrix factorization (NMF) has been a popular model for a wide range of signal processing and machine learning problems. It is usually formulated as a nonconvex cost minimization problem. This work settles the convergence issue of a popular algorithm based on the alternating direction method of multipliers proposed in Boyd et al 2011. We show that the algorithm converges globally to the set of KKT solutions whenever certain penalty parameter ρ satisfies ρ > 1. We further extend the algorithm and its analysis to the problem where the observation matrix contains missing values. Numerical experiments on real and synthetic data sets demonstrate the effectiveness of the algorithms under investigation.

We study a stochastic and distributed algorithm for nonconvex problems whose objective consists a sum $N$ nonconvex $L_i/N$-smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into $N$ subproblems, and utilizes an augmented Lagrangian based primal-dual scheme to solve it in a distributed and stochastic manner. With a special non-uniform sampling, a version of NESTT achieves $\epsilon$-stationary solution using $\mathcal{O}((\sum_{i=1}^N\sqrt{L_i/N})^2/\epsilon)$ gradient evaluations, which can be up to $\mathcal{O}(N)$ times better than the (proximal) gradient descent methods. It also achieves Q-linear convergence rate for nonconvex $\ell_1$ penalized quadratic problems with polyhedral constraints. Further, we reveal a fundamental connection between {\it primal-dual} based methods and a few {\it primal only} methods such as IAG/SAG/SAGA.