We introduce Local Reinforcement-Based Selection of Auxiliary Objectives (LRSAO), a novel approach that selects auxiliary objectives using reinforcement learning (RL) to support the optimization process of an evolutionary algorithm (EA) as in EA+RL framework and furthermore incorporates the ability to unlearn previously used objectives. By modifying the reward mechanism to penalize moves that do no increase the fitness value and relying on the local auxiliary objectives, LRSAO dynamically adapts its selection strategy to optimize performance according to the landscape and unlearn previous objectives when necessary.

We address the challenge of actively ranking a set of items/players with varying values/strengths. The comparison outcomes are random, with a greater noise the closer the values. A crucial requirement is that, at each iteration of the algorithm, all items must be compared once, i.e., an iteration is a perfect matching. Furthermore, we presume that comparing two players with closely matched strengths incurs no cost and, in contrast, a unit cost is associated with comparing players whose strength difference is more substantial. Our secondary objective is to determine an optimal matching between players based on this cost function: we propose and analyze an algorithm that draws on concepts from both AKS sorting networks and bandit theory. Our algorithm achieves both objectives with high probability, and the total cost is optimal (up to logarithmic terms).

Aggregated hold-out (agghoo) is a method which averages learning rules selected by hold-out (that is, cross-validation with a single split). We provide the first theoretical guarantees on agghoo, ensuring that it can be used safely: Agghoo performs at worst like the hold-out when the risk is convex. The same holds true in classification with the 0--1 risk, with an additional constant factor. For the hold-out, oracle inequalities are known for bounded losses, as in binary classification. We show that similar results can be proved, under appropriate assumptions, for other risk-minimization problems. In particular, we obtain an oracle inequality for regularized kernel regression with a Lipschitz loss, without requiring that the $Y$ variable or the regressors be bounded. Numerical experiments show that aggregation brings a significant improvement over the hold-out and that agghoo is competitive with cross-validation.

Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance), with numerous successful applications. The representation is constructed as the expectation of the feature map defined by a kernel. As a mean, its classical empirical estimator, however, can be arbitrary severely affected even by a single outlier in case of unbounded features. To the best of our knowledge, unfortunately even the consistency of the existing few techniques trying to alleviate this serious sensitivity bottleneck is unknown. In this paper, we show how the recently emerged principle of median-of-means can be used to design estimators for kernel mean embedding and MMD with excessive resistance properties to outliers, and optimal sub-Gaussian deviation bounds under mild assumptions.

This paper studies $V$-fold cross-validation for model selection in least-squares density estimation. The goal is to provide theoretical grounds for choosing $V$ in order to minimize the least-squares loss of the selected estimator. We first prove a non-asymptotic oracle inequality for $V$-fold cross-validation and its bias-corrected version ($V$-fold penalization). In particular, this result implies that $V$-fold penalization is asymptotically optimal in the nonparametric case. Then, we compute the variance of $V$-fold cross-validation and related criteria, as well as the variance of key quantities for model selection performance. We show that these variances depend on $V$ like $1+4/(V-1)$, at least in some particular cases, suggesting that the performance increases much from $V=2$ to $V=5$ or $10$, and then is almost constant. Overall, this can explain the common advice to take $V=5\,$---at least in our setting and when the computational power is limited---, as supported by some simulation experiments. An oracle inequality and exact formulas for the variance are also proved for Monte- Carlo cross-validation, also known as repeated cross-validation, where the parameter $V$ is replaced by the number $B$ of random splits of the data.