On Local Regret

Online learning aims to perform nearly as well as the best hypothesis in hindsight. For some hypothesis classes, though, even finding the best hypothesis offline is challenging. In such offline cases, local search techniques are often employed and only local optimality guaranteed. For online decision-making with such hypothesis classes, we introduce local regret, a generalization of regret that aims to perform nearly as well as only nearby hypotheses. We then present a general algorithm to minimize local regret with arbitrary locality graphs. We also show how the graph structure can be exploited to drastically speed learning. These algorithms are then demonstrated on a diverse set of online problems: online disjunct learning, online Max-SAT, and online decision tree learning.Comment: This is the longer version of the same-titled paper appearing in the Proceedings of the Twenty-Ninth International Conference on Machine Learning (ICML), 201

Slow Learners are Fast

Online learning algorithms have impressive convergence properties when it comes to risk minimization and convex games on very large problems. However, they are inherently sequential in their design which prevents them from taking advantage of modern multi-core architectures. In this paper we prove that online learning with delayed updates converges well, thereby facilitating parallel online learning.Comment: Extended version of conference paper - NIPS 200

No-Regret Learning in Extensive-Form Games with Imperfect Recall

Counterfactual Regret Minimization (CFR) is an efficient no-regret learning algorithm for decision problems modeled as extensive games. CFR's regret bounds depend on the requirement of perfect recall: players always remember information that was revealed to them and the order in which it was revealed. In games without perfect recall, however, CFR's guarantees do not apply. In this paper, we present the first regret bound for CFR when applied to a general class of games with imperfect recall. In addition, we show that CFR applied to any abstraction belonging to our general class results in a regret bound not just for the abstract game, but for the full game as well. We verify our theory and show how imperfect recall can be used to trade a small increase in regret for a significant reduction in memory in three domains: die-roll poker, phantom tic-tac-toe, and Bluff.Comment: 21 pages, 4 figures, expanded version of article to appear in Proceedings of the Twenty-Ninth International Conference on Machine Learnin

Garnet to hydrogarnet: effect of post synthesis treatment on cation substituted LLZO solid electrolyte and its effect on Li ion conductivity

We investigated why commercial Li$_7$La$_3$Zr$_2$O$_{12}$ (LLZO) with Nb- and Ta substitution shows very low mobility on a local scale, as observed with temperature-dependent NMR techniques, compared to Al and W substituted samples, although impedance spectroscopy on sintered pellets suggests something else: conductivity values do not show a strong dependence on the type of substituting cation. We observed that mechanical treatment of these materials causes a symmetry reduction from garnet to hydrogarnet structure. To understand the impact of this lower symmetric structure in detail and its effect on the Li ion conductivity, neutron powder diffraction and $^6$Li NMR were utilized. Despite the finding that, in some materials, disorder can be beneficial with respect to ionic conductivity, pulsed-field gradient NMR measurements of the long-range transport indicate a higher Li$^+$ diffusion barrier in the lower symmetric hydrogarnet structure. The symmetry reduction can be reversed back to the higher symmetric garnet structure by annealing at 1100 °C. This unintended phase transition and thus a reduction in conductivity is crucial for the processing of LLZO materials in the fabrication of all-solid state batteries

Hop: Heterogeneity-Aware Decentralized Training

Recent work has shown that decentralized algorithms can deliver superior performance over centralized ones in the context of machine learning. The two approaches, with the main difference residing in their distinct communication patterns, are both susceptible to performance degradation in heterogeneous environments. Although vigorous efforts have been devoted to supporting centralized algorithms against heterogeneity, little has been explored in decentralized algorithms regarding this problem. This paper proposes Hop, the first heterogeneity-aware decentralized training protocol. Based on a unique characteristic of decentralized training that we have identified, the iteration gap, we propose a queue-based synchronization mechanism that can efficiently implement backup workers and bounded staleness in the decentralized setting. To cope with deterministic slowdown, we propose skipping iterations so that the effect of slower workers is further mitigated. We build a prototype implementation of Hop on TensorFlow. The experiment results on CNN and SVM show significant speedup over standard decentralized training in heterogeneous settings

Online Convex Programming and Generalized Infinitesimal Gradient Ascent

Convex programming involves a convex set F R and a convex function c : F ! R. The goal of convex programming is to nd a point in F which minimizes c. In this paper, we introduce online convex programming. In online convex programming, the convex set is known in advance, but in each step of some repeated optimization problem, one must select a point in F before seeing the cost function for that step. This can be used to model factory production, farm production, and many other industrial optimization problems where one is unaware of the value of the items produced until they have already been constructed. We introduce an algorithm for this domain, apply it to repeated games, and show that it is really a generalization of in nitesimal gradient ascent, and the results here imply that generalized in nitesimal gradient ascent (GIGA) is universally consistent