Optimal discovery with probabilistic expert advice: finite time analysis and macroscopic optimality

On the optimality of the Hedge algorithm in the stochastic regime

In this paper, we study the behavior of the Hedge algorithm in the online stochastic setting. We prove that anytime Hedge with decreasing learning rate, which is one of the simplest algorithm for the problem of prediction with expert advice, is surprisingly both worst-case optimal and adaptive to the easier stochastic and adversarial with a gap problems. This shows that, in spite of its small, non-adaptive learning rate, Hedge possesses the same optimal regret guarantee in the stochastic case as recently introduced adaptive algorithms. Moreover, our analysis exhibits qualitative differences wi…

On the asymptotic optimality of the comb strategy for prediction with expert advice

For the problem of prediction with expert advice in the adversarial setting with geometric stopping, we compute the exact leading order expansion for the long time behavior of the value function. Then, we use this expansion to prove that as conjectured in Gravin et al. [12], the comb strategies are indeed asymptotically optimal for the adversary in the case of 4 experts.

Experimental Evidence for Asymptotic Non-Optimality of Comb Adversary Strategy

For the problem of prediction with expert advice in the adversarial setting with finite stopping time, we give strong computer evidence that the comb strategy for $k=5$ experts is not asymptotically optimal, thereby giving strong evidence against a conjecture of Gravin, Peres, and Sivan.

通过结构实现神经可塑性：用于图组合优化的学习增强算法

Neural Tractability via Structure: Learning-Augmented Algorithms for Graph Combinatorial Optimization

本文提出一种结合神经模型与参数化算法的框架，通过结构分析提升图组合优化的解质量，实现高效且可靠的求解方法。

Optimal discovery with probabilistic expert advice

We consider an original problem that arises from the issue of security analysis of a power system and that we name optimal discovery with probabilistic expert advice. We address it with an algorithm based on the optimistic paradigm and the Good-Turing missing mass estimator. We show that this strategy uniformly attains the optimal discovery rate in a macroscopic limit sense, under some assumptions on the probabilistic experts. We also provide numerical experiments suggesting that this optimal behavior may still hold under weaker assumptions.

由专家建议预测引出的偏微分方程的数值求解

Numerical solution of a PDE arising from prediction with expert advice

本文通过数值求解与专家建议预测博弈相关的退化椭圆方程，利用对称性将计算维度提升至 n≤10，并提出 COMB 策略非最优等对抗策略最优性猜想。