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arXiv research

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.

168,742 papers · 148 categories

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69138206275 · Jun 202019922001200920172026
48 results for Gaussian rewards

The paper proves the convergence of Q-value for Gaussian rewards.

problem Existing proofs cannot guarantee convergence of the Q-function for Gaussian rewards.
method Using the central limit theorem and relaxing the condition to E[r(s,a)2]<E[r(s,a)^2]<\infty.
result Proves the convergence of the Q-function under the condition of E[r(s,a)2]<E[r(s,a)^2]<\infty.

Method predicts future rewards from past actions in a linear Gaussian system.

problem Maximizing cumulative reward in a stochastic multi-armed bandit with linear Gaussian dynamics.
method Proposes a method using a modified Kalman filter to predict future rewards based on past rewards.
result Reward from any action can be used to predict another action's future reward.

New algorithm reduces regret in multi-armed bandit problems with Gaussian rewards.

problem Optimizing decisions in multi-armed bandit problems with Gaussian rewards.
method Proposed TSCG and UTSCG algorithms using Thompson Sampling with Gaussian prior.
result Achieved lower regret bounds for optimal arm selection.

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.

A new method optimizes in nonstationary environments with many arms efficiently.

problem Optimizing in nonstationary environments with a large number of arms.
method Gaussian interpolation to learn continuous Lipschitz reward functions in nonstationary environments.
result Efficiently learns continuous Lipschitz reward functions with O(T)\mathcal{O}^*(\sqrt{T}) cumulative regret.

New algorithm uses machine learning to predict rewards for decision-making problems.

problem Sequential decision-making under uncertainty with scarce online data.
method Machine Learning-Assisted Upper Confidence Bound (MLA-UCB) algorithm.
result Proves to improve cumulative regret even with biased surrogate rewards.

Nonparametric Thompson Sampling achieves optimal regret for risk-averse bandits with sub-Gaussian rewards.

problem Optimizing risk-averse bandit problems with sub-Gaussian rewards.
method Anchor-free nonparametric Thompson Sampling algorithm ρextNPTSSGρ ext{-}NPTS_{\mathrm{SG}}.
result Achieves regret matching the instance-dependent lower bound to leading order in logn\log n.

We here adopt Bayesian nonparametric mixture models to extend multi-armed bandits in general, and Thompson sampling in particular, to scenarios where there is reward model uncertainty. In the stochastic multi-armed bandit, the reward for the played arm is generated from an unknown distribution. Reward uncertainty, i.e.…

2018-08-08abs ↗pdf ↗

Iterative tilting fine-tunes diffusion models for reward-tilted distributions.

problem Fine-tuning diffusion models for reward-tilted distributions.
method Decomposes large reward tilts into smaller, tractable tilts via first-order Taylor expansion, avoiding backpropagation.
result Validated on a two-dimensional Gaussian mixture, achieving exact closed-form solutions.

A bandit algorithm reduces regret in noisy, communication-constrained feedback.

problem Distributed stochastic multi-armed bandit with noisy, communication-constrained feedback.
method Proposes a multi-phase bandit algorithm, UE-UCB++, that matches an information-theoretic lower bound.
result Matches an information-theoretic lower bound of Ω(√(KT/σ²)) on the minimax regret.

A new algorithm balances global reward and group constraints in federated multi-armed bandits.

problem Maximizing global reward while protecting client privacy in federated learning.
method Combinatorial contextual bandit with group constraints, using a two-output Gaussian process.
result TCGP-UCB incurs low regret, balancing super arm reward and group reward constraints.

A new algorithm uses concavity in Gaussian processes to optimize decisions in bandit problems.

problem Optimizing decisions in sequential problems with context-dependent rewards.
method Proposes a UCB algorithm using a shape-constrained reward function estimator based on a Gaussian Process model with concavity constraints.
result Derives regret bounds for the proposed UCB algorithm.

The paper tackles resource allocation for arms with unknown and random rewards, achieving optimal regret bounds.

problem Allocating resources on arms with unknown and random rewards.
method Developed two algorithms with optimal regret bounds for b[0,1]b \in [0,1], demonstrating a phase transition at b=1/2b=1/2.
result Achieved optimal gap-dependent and gap-independent regret bounds for b[0,1]b \in [0,1].

New algorithms for generalized linear bandits with unknown reward functions.

problem Misspecification of reward functions in existing bandit algorithms.
method Introducing single index bandits, proposing STOR, ESTOR, and GSTOR algorithms.
result Achieved nearly optimal regret bound of ildeOT(T) ilde{O}_T(\sqrt{T}).

The study analyzes how neural reward models learn features for policy optimization in a Gaussian single-index model.

problem Reward modeling in policy optimization and its impact on downstream value.
method Two-stage neural reward model: first learns hidden direction, then fits readout layer.
result For any feature-learning temperature above a dimension-free threshold, a constant fraction of neurons recover the hidden direction.

The paper analyzes the reward improvement of aligned policies in large language models.

problem Optimizing policies in large language models while staying close to a reference policy.
method Information-theoretic analysis and reduction to exponential order statistics.
result Information-theoretic upper bounds on reward improvement are derived.

Polynomial-time method solves complex combinatorial semi-bandits.

problem Optimal strategies for combinatorial semi-bandits with uncorrelated Gaussian rewards.
method Proposes a polynomial-time method to solve the Graves-Lai optimization problem for various combinatorial structures.
result First known approach to implement asymptotically optimal algorithms in polynomial time for combinatorial semi-bandits.

This paper extends the MAB problem to consider risk-reward tradeoffs.

problem Maximizing reward while accounting for risk in multi-armed bandit problems.
method Introduced the Risk Aware Lower Confidence Bound (RALCB) algorithm to solve the mean-variance MAB problem.
result The RALCB algorithm performs better than the algorithm in Sani et al. (2012) in both independent and dependent scenarios.

We investigate the use of bootstrapping in the bandit setting. We first show that the commonly used non-parametric bootstrapping (NPB) procedure can be provably inefficient and establish a near-linear lower bound on the regret incurred by it under the bandit model with Bernoulli rewards. We show that NPB with an approp…

2018-05-24abs ↗pdf ↗

A novel approach uses an ensemble of Gaussian processes for robust and adaptive reinforcement learning.

problem Adaptive reinforcement learning in large or continuous state spaces.
method Online scalable (OS) approach with a weighted ensemble of Gaussian processes.
result The ensemble approach improves performance in adversarial settings.

Thompson Sampling shows polynomial regret for combinatorial semi-bandits with subgaussian rewards.

problem Finding optimal solutions in combinatorial semi-bandits with suboptimal sampling.
method Proposes Thompson Sampling with polynomial regret for linear combinatorial semi-bandits.
result Demonstrates 'mismatched sampling paradox' where knowing distributions can lead to worse performance.

Optimizing rewards under budget constraints with correlated costs and rewards.

problem Maximizing total expected reward under a budget constraint on total cost with correlated and potentially heavy-tailed cost-reward pairs.
method Proposes algorithms exploiting correlation between cost and reward via linear minimum mean-square error estimation to achieve tight regret bounds.
result Achieves O(logB)O(\log B) regret for a budget B>0B>0 under certain moment conditions.

KL-MS improves regret bounds for multi-armed bandits with bounded rewards.

problem Designing efficient exploration algorithms for multi-armed bandits with bounded rewards.
method Kullback-Leibler Maillard Sampling (KL-MS) for multi-armed bandits with bounded rewards.
result KL-MS achieves a worst-case regret bound of O(μ(1μ)KTlnK+KlnT)O(\sqrt{μ^*(1-μ^*) K T \ln K} + K \ln T).

We investigate and provide new insights on the sampling rule called Top-Two Thompson Sampling (TTTS). In particular, we justify its use for fixed-confidence best-arm identification. We further propose a variant of TTTS called Top-Two Transportation Cost (T3C), which disposes of the computational burden of TTTS. As our …

2019-10-24abs ↗pdf ↗

The stochastic multi-armed bandit problem is well understood when the reward distributions are sub-Gaussian. In this paper we examine the bandit problem under the weaker assumption that the distributions have moments of order 1+ε, for some ε(0,1]ε\in (0,1]. Surprisingly, moments of order 2 (i.e., finite variance) are suffi…

2012-09-08abs ↗pdf ↗

Improved GP bandit algorithms for noiseless, varying noise, and RKHS norms.

problem Minimizing regret in Gaussian process bandits with unknown reward functions.
method New upper bound on maximum posterior variance, refined MVR and PE algorithms.
result Optimal regret bounds for noiseless, varying noise, and RKHS norms.

Recent studies have shown that reinforcement learning (RL) models are vulnerable in various noisy scenarios. For instance, the observed reward channel is often subject to noise in practice (e.g., when rewards are collected through sensors), and is therefore not credible. In addition, for applications such as robotics, …

2018-10-02abs ↗pdf ↗

New algorithm for shareable arms with load-dependent rewards in stochastic bandits.

problem Learning optimal play strategy with shareable finite-capacity arms in stochastic bandits.
method Developed a capacity estimator and online learning algorithm for MP-MAB with shareable arms.
result Regret upper bound matches the lower bound, validating the algorithm's performance.

A novel algorithm minimizes regret in a multi-agent bandit problem with time-varying random graphs and heterogeneous rewards.

problem Minimizing regret in a multi-agent multi-armed bandit problem with time-varying random graphs and heterogeneous rewards.
method Introduces a novel algorithmic framework combining averaging-based consensus with a weighting technique and upper confidence bound.
result Derives optimal instance-dependent regret upper bounds of order logT\log{T} in both sub-gaussian and sub-exponential environments.

The paper proposes a model reward scheme for collaborative ML based on Shapley value and information gain.

problem Designing fair incentives for collaborative machine learning.
method The paper proposes a reward scheme based on Shapley value and information gain, with properties like fairness and stability.
result The proposed reward scheme satisfies fairness and trade-offs between desirable properties via an adjustable parameter.

New strategy optimally identifies best arm in unknown variance Gaussian bandits.

problem Identifying the best arm in two-armed Gaussian bandits with unknown variances.
method Proposes a Neyman Allocation (NA)-Augmented Inverse Probability weighting (AIPW) strategy to estimate variances and draw arms adaptively.
result Demonstrates asymptotic optimality of the proposed strategy in the small-gap regime.

Optimizes reward learning design for complex tasks using nonparametric methods.

problem Challenges in specifying reward functions for complex tasks.
method Models rewards and policies as nonparametric functions in RKHSs, derives risk bounds, and optimizes query design.
result Derives non-asymptotic excess risk bounds and finite sample statistical rates for reward learning.

Study on identifying most preferred policy in bandits with vector-valued rewards.

problem Identifying the most preferred policy in bandits with vector-valued rewards.
method Derive a novel lower bound on sample complexity, design the Preference-based Track and Stop (PreTS) algorithm, and derive a new concentration inequality.
result The sample complexity of PreTS is asymptotically tight.

We consider the sequential Bayesian optimization problem with bandit feedback, adopting a formulation that allows for the reward function to vary with time. We model the reward function using a Gaussian process whose evolution obeys a simple Markov model. We introduce two natural extensions of the classical Gaussian pr…

2016-01-25abs ↗pdf ↗

The paper identifies all ε-optimal arms in a bandit problem with Gaussian rewards.

problem Identifying all ε-optimal arms in a finite stochastic multi-armed bandit with Gaussian rewards.
method The paper provides two lower bounds and a Track-and-Stop strategy to solve the problem, with an efficient numerical method to solve the convex max-min program.
result The Track-and-Stop strategy has asymptotically optimal average sample complexity in the regime of low risk.

New algorithm reduces semi-bandit regret using covariance estimates.

problem Complexity of semi-bandits due to joint distribution of outcomes.
method Develops a new sub-exponential distribution family and an algorithm using covariance estimates.
result Proves a new lower bound on expected regret and constructs an algorithm with asymptotic analysis.

Improved Bayesian regret bound for linear Thompson sampling with general distributions.

problem Proving an improved Bayesian regret bound for linear Thompson sampling with general distributions.
method Generalized elliptical potential lemma for non-Gaussian noise and prior distributions.
result Minimax optimal regret bound for changing action sets with general prior and noise distributions.

Paper tackles constrained bandit problems with a new learning framework.

problem Optimizing a black-box reward function subject to a black-box constraint function over a continuous space.
method Rectified Pessimistic-Optimistic Learning (RPOL) framework, incorporating optimistic and pessimistic GP bandit learning.
result RPOL achieves sublinear regret and minimal cumulative constraint violation.