Adaptive Foundation Models for Online Decisions: HyperAgent with Fast Incremental Uncertainty Estimation

Foundation models often struggle with uncertainty when faced with new situations in online decision-making, necessitating scalable and efficient exploration to resolve this uncertainty. We introduce GPT-HyperAgent, an augmentation of GPT with HyperAgent for uncertainty-aware, scalable exploration in contextual bandits, a fundamental online decision problem involving natural language input. We prove that HyperAgent achieves fast incremental uncertainty estimation with $\tilde{O}(\log T)$ per-step computational complexity over $T$ periods under the linear realizable assumption. Our analysis demonstrates that HyperAgent's regret order matches that of exact Thompson sampling in linear contextual bandits, closing a significant theoretical gap in scalable exploration. Empirical results in real-world contextual bandit tasks, such as automated content moderation with human feedback, validate the practical effectiveness of GPT-HyperAgent for safety-critical decisions. Our code is open-sourced at \url{https://github.com/szrlee/GPT-HyperAgent/}.

Prior-dependent analysis of posterior sampling reinforcement learning with function approximation

This work advances randomized exploration in reinforcement learning (RL) with function approximation modeled by linear mixture MDPs. We establish the first prior-dependent Bayesian regret bound for RL with function approximation; and refine the Bayesian regret analysis for posterior sampling reinforcement learning (PSRL), presenting an upper bound of ${\mathcal{O}}(d\sqrt{H^3 T \log T})$, where $d$ represents the dimensionality of the transition kernel, $H$ the planning horizon, and $T$ the total number of interactions. This signifies a methodological enhancement by optimizing the $\mathcal{O}(\sqrt{\log T})$ factor over the previous benchmark (Osband and Van Roy, 2014) specified to linear mixture MDPs. Our approach, leveraging a value-targeted model learning perspective, introduces a decoupling argument and a variance reduction technique, moving beyond traditional analyses reliant on confidence sets and concentration inequalities to formalize Bayesian regret bounds more effectively.

Radar Anti-jamming Strategy Learning via Domain-knowledge Enhanced Online Convex Optimization

The dynamic competition between radar and jammer systems presents a significant challenge for modern Electronic Warfare (EW), as current active learning approaches still lack sample efficiency and fail to exploit jammer's characteristics. In this paper, the competition between a frequency agile radar and a Digital Radio Frequency Memory (DRFM)-based intelligent jammer is considered. We introduce an Online Convex Optimization (OCO) framework designed to illustrate this adversarial interaction. Notably, traditional OCO algorithms exhibit suboptimal sample efficiency due to the limited information obtained per round. To address the limitations, two refined algorithms are proposed, utilizing unbiased gradient estimators that leverage the unique attributes of the jammer system. Sub-linear theoretical results on both static regret and universal regret are provided, marking a significant improvement in OCO performance. Furthermore, simulation results reveal that the proposed algorithms outperform common OCO baselines, suggesting the potential for effective deployment in real-world scenarios.

Probability Tools for Sequential Random Projection

We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and high-dimensional nature of random variables, a byproduct of the adaptive mechanisms inherent in sequential decision processes. Our work features a novel construction of a stopped process, facilitating the analysis of a sequence of concentration events that are interconnected in a sequential manner. By employing the method of mixtures within a self-normalized process, derived from the stopped process, we achieve a desired non-asymptotic probability bound. This bound represents a non-trivial martingale extension of the Johnson-Lindenstrauss (JL) lemma, marking a pioneering contribution to the literature on random projection and sequential analysis.

Optimistic Thompson Sampling for No-Regret Learning in Unknown Games

This work tackles the complexities of multi-player scenarios in \emph{unknown games}, where the primary challenge lies in navigating the uncertainty of the environment through bandit feedback alongside strategic decision-making. We introduce Thompson Sampling (TS)-based algorithms that exploit the information of opponents' actions and reward structures, leading to a substantial reduction in experimental budgets -- achieving over tenfold improvements compared to conventional approaches. Notably, our algorithms demonstrate that, given specific reward structures, the regret bound depends logarithmically on the total action space, significantly alleviating the curse of multi-player. Furthermore, we unveil the \emph{Optimism-then-NoRegret} (OTN) framework, a pioneering methodology that seamlessly incorporates our advancements with established algorithms, showcasing its utility in practical scenarios such as traffic routing and radar sensing in the real world.

Simple, unified analysis of Johnson-Lindenstrauss with applications

In this work, we present a simple and unified analysis of the Johnson-Lindenstrauss (JL) lemma, a cornerstone in the field of dimensionality reduction critical for managing high-dimensional data. Our approach not only simplifies the understanding but also unifies various constructions under the JL framework, including spherical, binary-coin, sparse JL, Gaussian and sub-Gaussian models. This simplification and unification make significant strides in preserving the intrinsic geometry of data, essential across diverse applications from streaming algorithms to reinforcement learning. Notably, we deliver the first rigorous proof of the spherical construction's effectiveness and provide a general class of sub-Gaussian constructions within this simplified framework. At the heart of our contribution is an innovative extension of the Hanson-Wright inequality to high dimensions, complete with explicit constants, marking a substantial leap in the literature. By employing simple yet powerful probabilistic tools and analytical techniques, such as an enhanced diagonalization process, our analysis not only solidifies the JL lemma's theoretical foundation but also extends its practical reach, showcasing its adaptability and importance in contemporary computational algorithms.

HyperAgent: A Simple, Scalable, Efficient and Provable Reinforcement Learning Framework for Complex Environments

To solve complex tasks under resource constraints, reinforcement learning (RL) agents need to be simple, efficient, and scalable with (1) large state space and (2) increasingly accumulated data of interactions. We propose the HyperAgent, a RL framework with hypermodel, index sampling schemes and incremental update mechanism, enabling computation-efficient sequential posterior approximation and data-efficient action selection under general value function approximation beyond conjugacy. The implementation of \HyperAgent is simple as it only adds one module and one line of code additional to DDQN. Practically, HyperAgent demonstrates its robust performance in large-scale deep RL benchmarks with significant efficiency gain in terms of both data and computation. Theoretically, among the practically scalable algorithms, HyperAgent is the first method to achieve provably scalable per-step computational complexity as well as sublinear regret under tabular RL. The core of our theoretical analysis is the sequential posterior approximation argument, made possible by the first analytical tool for sequential random projection, a non-trivial martingale extension of the Johnson-Lindenstrauss lemma. This work bridges the theoretical and practical realms of RL, establishing a new benchmark for RL algorithm design.

Hidden Community Detection in Social Networks

We introduce a new paradigm that is important for community detection in the realm of network analysis. Networks contain a set of strong, dominant communities, which interfere with the detection of weak, natural community structure. When most of the members of the weak communities also belong to stronger communities, they are extremely hard to be uncovered. We call the weak communities the hidden community structure. We present a novel approach called HICODE (HIdden COmmunity DEtection) that identifies the hidden community structure as well as the dominant community structure. By weakening the strength of the dominant structure, one can uncover the hidden structure beneath. Likewise, by reducing the strength of the hidden structure, one can more accurately identify the dominant structure. In this way, HICODE tackles both tasks simultaneously. Extensive experiments on real-world networks demonstrate that HICODE outperforms several state-of-the-art community detection methods in uncovering both the dominant and the hidden structure. In the Facebook university social networks, we find multiple non-redundant sets of communities that are strongly associated with residential hall, year of registration or career position of the faculties or students, while the state-of-the-art algorithms mainly locate the dominant ground truth category. In the Due to the difficulty of labeling all ground truth communities in real-world datasets, HICODE provides a promising approach to pinpoint the existing latent communities and uncover communities for which there is no ground truth. Finding this unknown structure is an extremely important community detection problem.