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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.

168,695 papers · 148 categories

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3978117156 · Jun 202019922001200920172026
48 results for Polynomial Reward

Study non-linear combinatorial bandits with polynomial rewards, finding significant differences from linear cases.

problem Adversarial combinatorial bandits with general non-linear reward functions.
method Extending existing work on adversarial linear combinatorial bandits, analyzing minimax optimal regret for polynomial and non-polynomial reward functions.
result Minimax optimal regret bounds for adversarial combinatorial bandits with general non-linear reward functions.

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.

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.

Reward-poisoning attacks can force RL agents to learn bad policies, and we categorize and quantify their feasibility.

problem Reward-poisoning attacks can manipulate RL agents to learn undesirable policies.
method Categorize attacks by infinity-norm constraint, provide thresholds for feasibility, and develop adaptive attack strategies.
result Adaptive reward-poisoning attacks can achieve the nefarious policy in polynomial steps, while non-adaptive attacks require exponential steps.

New algorithm for reward-free RL with linear function approximation, reducing sample complexity.

problem Efficiently learning optimal policies without prior reward information in complex environments.
method Developed an algorithm for reward-free RL in linear Markov decision processes, proving sample complexity bounds.
result Polynomial sample complexity in feature dimension and planning horizon, independent of states and actions.

New algorithms for efficient learning with long-term rewards in contextual bandits.

problem Efficient learning with long-term rewards in contextual bandits.
method Proposes new algorithms leveraging sparsity to discover dependence patterns and arm parameters.
result Regret upper bounds for data-poor and data-rich regimes, showing improved sample complexity.

The paper tackles combinatorial pure exploration with various feedback structures and proposes efficient algorithms.

problem Identifying the optimal action in a combinatorial space with limited feedback and nonlinear rewards.
method Designs polynomial-time adaptive algorithms for CPE-BL and CPE-PL, providing sample complexity analyses.
result The proposed algorithms achieve sample complexity close to lower bounds and outperform existing methods.

Paper tackles efficient IRL in offline settings with polynomial samples and runtime.

problem Efficiently learning reward functions from expert demonstrations in offline settings.
method Adapting the pessimism principle for offline RL, achieving strong guarantees.
result Achieved efficient IRL in offline and online settings with polynomial samples and runtime.

We consider Markov Decision Processes (MDPs) where the rewards are unknown and may change in an adversarial manner. We provide an algorithm that achieves state-of-the-art regret bound of O(τ(lnS+lnA)Tln(T))O( \sqrt{τ(\ln|S|+\ln|A|)T}\ln(T)), where SS is the state space, AA is the action space, ττ is the mixing time of the MDP, and $…

2019-05-25abs ↗pdf ↗

The paper develops a robust algorithm for contextual bandits with heavy-tailed rewards.

problem Contextual bandits with heavy-tailed rewards.
method Develops an algorithm based on Catoni's estimator for robust statistics, applying it to contextual bandits with general function approximation.
result Establishes regret bounds that depend on cumulative reward variance and logarithmically on the reward range and number of rounds.

Improves RLHF sample efficiency by scaling reward complexity polynomially.

problem Exponential sample complexity in RLHF algorithms for skewed preferences.
method SE-POPO, an online RLHF algorithm that achieves polynomial sample complexity.
result SE-POPO outperforms existing algorithms in sample efficiency.

This work shows how approximate reward models can significantly improve inference-time scaling.

problem Improving the efficiency of inference for large language models.
method Identifying the Bellman error of approximate reward models and using Sequential Monte Carlo (SMC) for inference.
result Approximate reward models can reduce computational complexity from exponential to polynomial in TT.

Polynomial chaos surrogates quantify epistemic uncertainty in AI-driven scientific models.

problem Uncertainty in reward estimates hinders interpretability in sequential generative models.
method Fit polynomial chaos expansions to trained models to propagate epistemic uncertainty and quantify sensitivity.
result Interpretable decomposition of reward components driving generative decisions.

ETGL-DDPG improves DDPG for sparse reward control with new exploration and replay techniques.

problem Sparse reward continuous control in reinforcement learning.
method Introduces εtεt-greedy search and GDRB framework for efficient exploration and reward use.
result ETGL-DDPG outperforms DDPG and other methods on sparse-reward continuous benchmarks.

New algorithm reduces reinforcement learning regret to sqrt(T) without strong dynamics assumptions.

problem Infinite-horizon average-reward reinforcement learning with linear MDPs.
method Approximate by discounted-reward MDPs and apply optimistic value iteration.
result Achieves O(sqrt(T)) regret with polynomial complexity.

The paper enhances preference learning by incorporating response time data.

problem Lack of temporal information in user decision-making for reward model learning.
method Integrates response time alongside binary choice data using the EZ model and Neyman-orthogonal loss functions.
result Response time-augmented approach reduces error rates from exponential to polynomial scaling, improving sample efficiency.

Paper develops methods to optimize policies directly from human feedback without reward inference.

problem Challenges in RLHF, including reward model overfitting and distribution shift.
method Develops two algorithms for RLHF without reward inference, using zeroth-order gradient approximators.
result Establishes polynomial convergence rates and outperforms existing methods in numerical experiments.

New algorithm for RL with horizon-free reward-free exploration for linear MDPs.

problem Reward-free reinforcement learning with long planning horizons.
method Uncertainty-weighted value-targeted regression with exploration-driven pseudo-reward and moment estimator.
result Horizon-free sample complexity of O(d2ε2)O(d^2\varepsilon^{-2}) for finding an ε\varepsilon-optimal policy.

The explore{exploit dilemma is one of the central challenges in Reinforcement Learning (RL). Bayesian RL solves the dilemma by providing the agent with information in the form of a prior distribution over environments; however, full Bayesian planning is intractable. Planning with the mean MDP is a common myopic approxi…

2012-03-15abs ↗pdf ↗

Paper resolves bias in ALFT training using generalized alignment games.

problem Systematic bias in estimating logarithmic rewards from small batches.
method Generalized Distributional Alignment Games, U-statistics, minimax polynomial estimators, Variance-Optimal Augmented Polynomial Optimization Program (AQP) Estimator.
result Proves optimal bias and accelerated convergence in ALFT training.

This paper investigates teacher hacking during language model distillation and proposes methods to mitigate it.

problem Teacher hacking during language model distillation, leading to suboptimal performance.
method A controlled experimental setup involving an oracle LM, teacher LM, and student LM, using fixed offline or online data generation techniques.
result Data diversity is the key factor in preventing teacher hacking during distillation.

Algorithm learns near-optimal policies for reward-mixing MDPs with few latent contexts.

problem Episodic reinforcement learning in reward-mixing Markov decision processes with a few latent contexts.
method Sample-efficient algorithm EM^2 using higher-order method-of-moments approach.
result Provides an ε-optimal policy using O(ε^(-2) * S^d A^d * poly(H, Z)^d) episodes for arbitrary M ≥ 2.

We consider a novel stochastic multi-armed bandit setting, where playing an arm makes it unavailable for a fixed number of time slots thereafter. This models situations where reusing an arm too often is undesirable (e.g. making the same product recommendation repeatedly) or infeasible (e.g. compute job scheduling on ma…

2019-07-27abs ↗pdf ↗

The paper tackles non-stationary MAB with periodic rewards.

problem Non-stationary mean rewards over time in a business context.
method Combines Fourier analysis with confidence-bound learning to estimate periods and minimize regret.
result Proposes a near-optimal policy with a regret bound of O(Tk=1KTk)O(\sqrt{T\sum_{k=1}^K T_k}).

New method for efficient online exploration in RLHF reduces regret.

problem Efficiently collecting new preference data in RLHF to refine reward model and policy.
method Proposes a new exploration scheme that directs preference queries toward reducing uncertainty in reward differences most relevant to policy improvement.
result Establishes regret bounds of order T(β+1)/(β+2)T^{(β+1)/(β+2)} for online RLHF, with polynomial scaling in all model parameters.

New algorithm reduces combinatorial semi-bandit regret efficiently.

problem Optimizing rewards from uncorrelated items in combinatorial semi-bandits.
method Developed an approximate version of ESCB with polynomial complexity.
result Achieved statistically efficient and polynomial time algorithm for combinatorial semi-bandits.

Trajectory-level supervision allows efficient offline reinforcement learning.

problem Offline reinforcement learning
method Developing a statistical theory for offline policy optimization from trajectory-level labels
result Proving a high-probability guarantee of order O~(H2Csa(π)/n)\widetilde O(H^2\sqrt{C_{sa}(\pi^\star)/n})

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.

Algorithm learns diffusion processes with high-dimensional state spaces.

problem Stochastic control of unbounded diffusion processes with high-dimensional state spaces.
method Adaptive partitioning and learning algorithm that refines discretization based on estimation bias and statistical confidence.
result Established regret bounds that depend on problem parameters, extending to unbounded diffusion processes.

In this paper, we study the stochastic combinatorial multi-armed bandit (CMAB) framework that allows a general nonlinear reward function, whose expected value may not depend only on the means of the input random variables but possibly on the entire distributions of these variables. Our framework enables a much larger c…

2016-10-20abs ↗pdf ↗

In many settings (e.g., robotics) demonstrations provide a natural way to specify tasks; however, most methods for learning from demonstrations either do not provide guarantees that the artifacts learned for the tasks, such as rewards or policies, can be safely composed and/or do not explicitly capture history dependen…

2019-07-26abs ↗pdf ↗

We consider a stochastic continuum armed bandit problem where the arms are indexed by the 2\ell_2 ball Bd(1+ν)B_{d}(1+ν) of radius 1+ν1+ν in Rd\mathbb{R}^d. The reward functions r:Bd(1+ν)Rr :B_{d}(1+ν) \rightarrow \mathbb{R} are considered to intrinsically depend on kdk \ll d unknown linear parameters so that $r(\mathbf{x}) = g(\ma…

2013-12-01abs ↗pdf ↗

We describe a novel algorithm for noisy global optimisation and continuum-armed bandits, with good convergence properties over any continuous reward function having finitely many polynomial maxima. Over such functions, our algorithm achieves square-root regret in bandits, and inverse-square-root error in optimisation, …

2013-02-11abs ↗pdf ↗

We introduce a new class of reinforcement learning methods referred to as {\em episodic multi-armed bandits} (eMAB). In eMAB the learner proceeds in {\em episodes}, each composed of several {\em steps}, in which it chooses an action and observes a feedback signal. Moreover, in each step, it can take a special action, c…

2015-08-04abs ↗pdf ↗

Adaptive algorithm identifies best arm with abstention, showing phase transition from polynomial to exponential error probability.

problem Bayesian best-arm identification with abstention to reduce undetected error.
method Adaptive algorithm PGWS that optimally uses abstention budget.
result Introducing any positive abstention budget induces an exponential decay in undetected error probability.

New algorithm learns causal graph to minimize regret in bandits without full structure.

problem Learning optimal decisions in bandits with unknown causal graph and latent confounders.
method Two-stage approach: first learns ancestors and necessary confounders, second applies standard bandit algorithm.
result No full causal structure needed for optimal decisions; only necessary confounders are crucial.

Contextual multi-armed bandit algorithms are widely used in sequential decision tasks such as news article recommendation systems, web page ad placement algorithms, and mobile health. Most of the existing algorithms have regret proportional to a polynomial function of the context dimension, dd. In many applications ho…

2019-07-26abs ↗pdf ↗

We characterize value functions in partially observable MDPs as semi-algebraic sets.

problem Understanding feasible value functions in partially observable Markov decision processes.
method Characterization of feasible value functions as semi-algebraic sets defined by polynomial inequalities.
result The feasible set of value functions in POMDPs is a semi-algebraic set, not a polytope as in MDPs.

Efficient algorithm for online learning with Massart noise achieves near-optimal mistake bound.

problem Online learning with adversarial context and Massart noise.
method Developed an efficient algorithm for γγ-margin linear classifiers in the presence of Massart noise.
result Achieved a mistake bound of ηT+o(T)ηT + o(T) for the online learning model.