In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Ex Input:
Traditional algorithms for stochastic optimization require projecting the solution at each iteration into a given domain to ensure its feasibility. When facing complex domains, such as positive semi-definite cones, the projection operation can be expensive, leading to a high computational cost per iteration. In this paper, we present a novel algorithm that aims to reduce the number of projections for stochastic optimization. The proposed algorithm combines the strength of several recent developments in stochastic optimization, including mini-batch, extra-gradient, and epoch gradient descent, in order to effectively explore the smoothness and strong convexity. We show, both in expectation and with a high probability, that when the objective function is both smooth and strongly convex, the proposed algorithm achieves the optimal O(1/T ) rate of convergence with only O(log T ) projections. Our empirical study verifies the theoretical result.

Ex Output:
O(logT ) Projections for Stochastic Optimization of Smooth and Strongly Convex Functions


Ex Input:
Many real-world decision-theoretic planning problems can be naturally modeled with discrete and continuous state Markov decision processes (DC-MDPs). While previous work has addressed automated decision-theoretic planning for DCMDPs, optimal solutions have only been defined so far for limited settings, e.g., DC-MDPs having hyper-rectangular piecewise linear value functions. In this work, we extend symbolic dynamic programming (SDP) techniques to provide optimal solutions for a vastly expanded class of DCMDPs. To address the inherent combinatorial aspects of SDP, we introduce the XADD — a continuous variable extension of the algebraic decision diagram (ADD) — that maintains compact representations of the exact value function. Empirically, we demonstrate an implementation of SDP with XADDs on various DC-MDPs, showing the first optimal automated solutions to DCMDPs with linear and nonlinear piecewise partitioned value functions and showing the advantages of constraint-based pruning for XADDs.

Ex Output:
Symbolic Dynamic Programming for Discrete and Continuous State MDPs


Ex Input:
This paper studies convolutional networks that require limited computational resources at test time. We develop a new network architecture that performs on par with state-of-the-art convolutional networks, whilst facilitating prediction in two settings: (1) an anytime-prediction setting in which the network’s prediction for one example is progressively updated, facilitating the output of a prediction at any time; and (2) a batch computational budget setting in which a fixed amount of computation is available to classify a set of examples that can be spent unevenly across “easier” and “harder” examples. Our network architecture uses multi-scale convolutions and progressively growing feature representations, which allows for the training of multiple classifiers at intermediate layers of the network. Experiments on three image-classification datasets demonstrate the efficacy of our architecture, in particular, when measured in terms of classification accuracy as a function of the amount of compute available.

Ex Output:

Multi-Scale Dense Convolutional Networks for Efficient Prediction