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.

Input: Consider Input: Potential games and decentralised partially observable MDPs (Dec–POMDPs) are two commonly used models of multi–agent interaction, for static optimisation and sequential decision– making settings, respectively. In this paper we introduce filtered fictitious play for solving repeated potential games in which each player’s observations of others’ actions are perturbed by random noise, and use this algorithm to construct an online learning method for solving Dec–POMDPs. Specifically, we prove that noise in observations prevents standard fictitious play from converging to Nash equilibrium in potential games, which also makes fictitious play impractical for solving Dec–POMDPs. To combat this, we derive filtered fictitious play, and provide conditions under which it converges to a Nash equilibrium in potential games with noisy observations. We then use filtered fictitious play to construct a solver for Dec–POMDPs, and demonstrate our new algorithm’s performance in a box pushing problem. Our results show that we consistently outperform the state–of–the–art Dec– POMDP solver by an average of 100% across the range of noise in the observation function.

Output: Filtered Fictitious Play for Perturbed Observation Potential Games and Decentralised POMDPs


Input: Consider Input: Self-paced learning (SPL) has been attracting increasing attention in machine learning and computer vision. Albeit empirically substantiated to be effective, the investigation on its theoretical insight is still a blank. It is even unknown that what objective a general SPL regime converges to. To this issue, this study attempts to initially provide some new insights under this “heuristic” learning scheme. Specifically, we prove that the solving strategy on SPL exactly accords with a majorization minimization algorithm, a well known technique in optimization and machine learning, implemented on a latent objective. A more interesting finding is that, the loss function contained in this latent objective has a similar configuration with non-convex regularized penalty, an attractive topic in statistics and machine learning. In particular, we show that the previous hard and linear self-paced regularizers are equivalent to the capped norm and minimax concave plus penalties, respectively, both being widely investigated in statistics. Such connections between SPL and previous known researches enhance new insightful comprehension on SPL, like convergence and parameter setting rationality. The correctness of the proposed theory is substantiated by experimental results on synthetic and UCI data sets.

Output: What Objective Does Self-paced Learning Indeed Optimize?


Input: Consider Input: We present a new decision rule, maximin safety, that seeks to maintain a large margin from the worst outcome, in much the same way minimax regret seeks to minimize distance from the best. We argue that maximin safety is valuable both descriptively and normatively. Descriptively, maximin safety explains the well-known decoy effect, in which the introduction of a dominated option changes preferences among the other options. Normatively, we provide an axiomatization that characterizes preferences induced by maximin safety, and show that maximin safety shares much of the same behavioral basis with minimax regret.


Output: Maximin Safety: When Failing to Lose is Preferable to Trying to Win