A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Algorithm BGLM-OFU minimizes regret in combinatorial causal bandits with binary models.
problem Minimizing expected regret in combinatorial causal bandits with binary generalized linear models.
method BGLM-OFU algorithm based on maximum likelihood estimation for Markovian BGLMs, and causal inference techniques for linear models with hidden variables.
result Achieves O(TlogT) regret for binary generalized linear models.
Unified framework for ensemble sampling in nonlinear contextual bandits with provable regret bounds.
problem Efficient exploration in nonlinear contextual bandits with unknown feature dimensions.
method Developed GLM-ES and Neural-ES for generalized linear and neural contextual bandits, respectively, using maximum likelihood estimation on randomly perturbed data.
result Unified high-probability frequentist regret bounds for GLM-ES and Neural-ES, matching state-of-the-art results.
The normalized maximized likelihood (NML) provides the minimax regret solution in universal data compression, gambling, and prediction, and it plays an essential role in the minimum description length (MDL) method of statistical modeling and estimation. Here we show that the normalized maximum likelihood has a Bayes-li…
Thompson Sampling bounds for contextual bandits with sub-Gaussian rewards.
problem Improving the performance of Thompson Sampling in contextual bandits with sub-Gaussian rewards.
method Proved comprehensive bounds on Thompson Sampling expected cumulative regret based on mutual information and lifted information ratio for sub-Gaussian rewards.
result Explicit regret bounds for various contextual bandit scenarios.
In this note, we present a version of the Thompson sampling algorithm for the problem of online linear generalization with full information (i.e., the experts setting), studied by Kalai and Vempala, 2005. The algorithm uses a Gaussian prior and time-varying Gaussian likelihoods, and we show that it essentially reduces …
Study optimal policy regret in partially observable Markov games with adaptive opponents.
problem Optimal sequential decision-making in partially observable environments against strategic, adaptive opponents.
method An epoch-based optimistic maximum-likelihood algorithm that selects one policy per epoch using confidence sets built cumulatively from past data.
result Achieves ildeO(T) policy regret for fixed problem parameters, with explicit dependence on horizon, adversary memory, confidence radius, and aggregate Eluder dimension.
Inspired by the Reward-Biased Maximum Likelihood Estimate method of adaptive control, we propose RBMLE -- a novel family of learning algorithms for stochastic multi-armed bandits (SMABs). For a broad range of SMABs including both the parametric Exponential Family as well as the non-parametric sub-Gaussian/Exponential f…
The paper explores how over-parameterized linear regression models generalize without violating learning theory principles.
problem Understanding how over-parameterized linear regression models generalize without violating learning theory principles.
method The paper uses the predictive normalized maximum likelihood (pNML) learner to investigate the minimum norm solution of over-parameterized linear regression models.
result The model generalizes well when the test sample lies in a subspace spanned by eigenvectors associated with large eigenvalues of the training data.
The Predictive Normalized Maximum Likelihood (pNML) scheme has been recently suggested for universal learning in the individual setting, where both the training and test samples are individual data. The goal of universal learning is to compete with a ``genie'' or reference learner that knows the data values, but is res…
Contextual bandits are widely used in Internet services from news recommendation to advertising, and to Web search. Generalized linear models (logistical regression in particular) have demonstrated stronger performance than linear models in many applications where rewards are binary. However, most theoretical analyses …
We consider stochastic multi-armed bandit problems with complex actions over a set of basic arms, where the decision maker plays a complex action rather than a basic arm in each round. The reward of the complex action is some function of the basic arms' rewards, and the feedback observed may not necessarily be the rewa…
This paper tackles sample-efficient reinforcement learning for partially observable Markov games.
problem Learning in partially observable Markov games with incomplete information.
method A simple algorithm combining optimism and Maximum Likelihood Estimation (MLE) for self-play, and a variant of optimistic MLE for adversarial opponents.
result The proposed algorithms achieve approximate Nash, correlated, and coarse correlated equilibria in polynomial samples for weakly revealing POMGs.
We study the pricing problem faced by a firm that sells a large number of products, described via a wide range of features, to customers that arrive over time. Customers independently make purchasing decisions according to a general choice model that includes products features and customers' characteristics, encoded as…
We investigate the piecewise-stationary combinatorial semi-bandit problem. Compared to the original combinatorial semi-bandit problem, our setting assumes the reward distributions of base arms may change in a piecewise-stationary manner at unknown time steps. We propose an algorithm, \texttt{GLR-CUCB}, which incorporat…
Cascading bandit (CB) is a popular model for web search and online advertising, where an agent aims to learn the K most attractive items out of a ground set of size L during the interaction with a user. However, the stationary CB model may be too simple to apply to real-world problems, where user preferences may ch…
Study dynamic assortment and positioning of products with varying display effects.
problem Dynamic assortment and positioning of products with varying display effects.
method Design round-based learning algorithms for both multiplicative and general position effects models, and develop efficient subroutines for optimization.
result First regret-optimal characterization for both models, with matching upper and lower bounds.