Gaussian Process Planning with Lipschitz Continuous Reward Functions: Towards Unifying Bayesian Optimization, Active Learning, and Beyond

This paper presents a novel nonmyopic adaptive Gaussian process planning (GPP) framework endowed with a general class of Lipschitz continuous reward functions that can unify some active learning/sensing and Bayesian optimization criteria and offer practitioners some flexibility to specify their desired choices for defining new tasks/problems. In particular, it utilizes a principled Bayesian sequential decision problem framework for jointly and naturally optimizing the exploration-exploitation trade-off. In general, the resulting induced GPP policy cannot be derived exactly due to an uncountable set of candidate observations. A key contribution of our work here thus lies in exploiting the Lipschitz continuity of the reward functions to solve for a nonmyopic adaptive epsilon-optimal GPP (epsilon-GPP) policy. To plan in real time, we further propose an asymptotically optimal, branch-and-bound anytime variant of epsilon-GPP with performance guarantee. We empirically demonstrate the effectiveness of our epsilon-GPP policy and its anytime variant in Bayesian optimization and an energy harvesting task.Comment: 30th AAAI Conference on Artificial Intelligence (AAAI 2016), Extended version with proofs, 17 page

Large Scale Learning of Agent Rationality in Two-Player Zero-Sum Games

With the recent advances in solving large, zero-sum extensive form games, there is a growing interest in the inverse problem of inferring underlying game parameters given only access to agent actions. Although a recent work provides a powerful differentiable end-to-end learning frameworks which embed a game solver within a deep-learning framework, allowing unknown game parameters to be learned via backpropagation, this framework faces significant limitations when applied to boundedly rational human agents and large scale problems, leading to poor practicality. In this paper, we address these limitations and propose a framework that is applicable for more practical settings. First, seeking to learn the rationality of human agents in complex two-player zero-sum games, we draw upon well-known ideas in decision theory to obtain a concise and interpretable agent behavior model, and derive solvers and gradients for end-to-end learning. Second, to scale up to large, real-world scenarios, we propose an efficient first-order primal-dual method which exploits the structure of extensive-form games, yielding significantly faster computation for both game solving and gradient computation. When tested on randomly generated games, we report speedups of orders of magnitude over previous approaches. We also demonstrate the effectiveness of our model on both real-world one-player settings and synthetic data

Effects of kefirs on glycemic, insulinemic and satiety responses

We hypothesized that three types of kefir (Lifewayy Low Fat Strawberry Kefir, ProBugs Kefir, orange flavor, and Lifewayy Low Fat Plain Kefir) would have low glycemic index (GI), high insulinemic index (II) and high satiety index (SI). Secondarily, we hypothesized that there would be no significant correlations among postprandial satiety, glucose and insulin responses. Lastly, we hypothesized that kefir, like other dairy products, would have dissociation of GI and II. To test our hypotheses, this study was divided into three phases. In Phase I, a portion of Lifewayy Low Fat Strawberry Kefir (S group) and a portion of ProBugs Kefir, orange flavor (O group) containing 50 g of available carbohydrates were tested. In Phase II, a portion of Lifewayy Low Fat Plain Kefir (P group) containing 25 g of available carbohydrates were tested. In Phase III, 240-kcals portions of all three types of kefirs were tested. In all phases a single meal, randomized crossover design was performed in which the test meals were fed to 10 healthy, male and female adults. The total glucose AUC of S group (p\u3c 0.0023), O group (p\u3c 0.0002) and P group (p\u3c 0.0002) were significantly lower compared with their respective glucose controls. A slight, but not significant inverse relationship between glycemic and satiety responses was observed with kefir beverages (r = -0.87; P = 0.13). Using a variance of component analysis, it was found that in the future, a significant relationship between the correlated effects of the treatments on GI and SI can be further tested by increasing the number of subjects to 12. Like other dairy products, kefir showed a dissociation of GI and II. Kefir can potentially be a useful food choice for patients with diabetes who are required to control their blood glucose levels