Bayesian optimization (BO) conventionally relies on handcrafted acquisition functions (AFs) to sequentially determine the sample points. However, it has been widely observed in practice that the best-performing AF in terms of regret can vary significantly under different types of black-box functions. It has remained a challenge to design one AF that can attain the best performance over a wide variety of black-box functions. This paper aims to attack this challenge through the perspective of reinforced few-shot AF learning (FSAF). Specifically, we first connect the notion of AFs with Q-functions and view a deep Q-network (DQN) as a surrogate differentiable AF. While it serves as a natural idea to combine DQN and an existing few-shot learning method, we identify that such a direct combination does not perform well due to severe overfitting, which is particularly critical in BO due to the need of a versatile sampling policy. To address this, we present a Bayesian variant of DQN with the following three features: (i) It learns a distribution of Q-networks as AFs based on the Kullback-Leibler regularization framework. This inherently provides the uncertainty required in sampling for BO and mitigates overfitting.

Bayesian optimization (BO) conventionally relies on handcrafted acquisition functions (AFs) to sequentially determine the sample points. However, it has been widely observed in practice that the best-performing AF in terms of regret can vary significantly under different types of black-box functions. It has remained a challenge to design one AF that can attain the best performance over a wide variety of black-box functions.

In many scenarios of binary classification, only positive instances are provided in the training data, leaving the rest of the data unlabeled. This setup, known as positive-unlabeled (PU) learning, is addressed here with a network flow-based method which utilizes pairwise similarities between samples. The method we propose here, 2-HNC, leverages Hochbaum's Normalized Cut (HNC) and the set of solutions it provides by solving a parametric minimum cut problem. The set of solutions, that are nested partitions of the samples into two sets, correspond to varying tradeoff values between the two goals: high intra-similarity inside the sets and low inter-similarity between the two sets. This nested sequence is utilized here to deliver a ranking of unlabeled samples by their likelihood of being negative. Building on this insight, our method, 2-HNC, proceeds in two stages. The first stage generates this ranking without assuming any negative labels, using a problem formulation that is constrained only on positive labeled samples. The second stage augments the positive set with likely-negative samples and recomputes the classification. The final label prediction selects among all generated partitions in both stages, the one that delivers a positive class proportion, closest to a prior estimate of this quantity, which is assumed to be given. Extensive experiments across synthetic and real datasets show that 2-HNC yields strong performance and often surpasses existing state-of-the-art algorithms.

Multi-task reinforcement learning often relies on task metadata -- such as brief natural-language descriptions -- to guide behavior across diverse objectives. We present Lexical Policy Networks (LEXPOL), a language-conditioned mixture-of-policies architecture for multi-task RL. LEXPOL encodes task metadata with a text encoder and uses a learned gating module to select or blend among multiple sub-policies, enabling end-to-end training across tasks. On MetaWorld benchmarks, LEXPOL matches or exceeds strong multi-task baselines in success rate and sample efficiency, without task-specific retraining. To analyze the mechanism, we further study settings with fixed expert policies obtained independently of the gate and show that the learned language gate composes these experts to produce behaviors appropriate to novel task descriptions and unseen task combinations. These results indicate that natural-language metadata can effectively index and recombine reusable skills within a single policy.

Many data applications involve counting queries, where a client specifies a feasible range of variables and a database returns the corresponding item counts. A program that produces the counts of different queries often risks leaking sensitive individual-level information. A popular approach to enhance data privacy is to return a noisy version of the actual count. It is typically achieved by adding independent noise to each query and then control the total privacy budget within a period. This approach may be limited in the number of queries and output accuracy in practice. Also, the returned counts do not maintain the total order for nested queries, an important feature in many applications. This work presents the design and analysis of a new method, sigma-counting, that addresses these challenges. Sigma-counting uses the notion of sigma-algebra to construct privacy-preserving counting queries. We show that the proposed concepts and methods can significantly improve output accuracy while maintaining a desired privacy level in the presence of massive queries to the same data. We also discuss how the technique can be applied to address large and time-varying datasets.