Optimal algorithms for non-linear ridge bandits reduce burn-in cost.
problem Non-linear models introduce a burn-in period with fixed cost.
method Two-stage algorithm: find initial action, then treat locally linear.
result Two-stage algorithm is statistically optimal.
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.
Kernel ε ε ε -Greedy optimizes multi-armed bandits with covariates for sub-linear regret.
problem Optimizing multi-armed bandits with covariates in a reproducing kernel Hilbert space.
method Online weighted kernel ridge regression estimator for mean reward function estimation.
result Achieves sub-linear regret rate and optimal T \sqrt{T} T regret rate under margin condition. Bayesian optimization improved for biased data.
problem Adversarial bias in observations, especially hidden confounders.
method Reduction to dueling bandits, information-directed sampling (IDS).
result First efficient kernelized algorithm with regret guarantees.
DART optimizes subset selection in non-linear bandit problems.
problem Optimizing subset selection in non-linear bandit problems with correlated rewards.
method DART algorithm for combinatorial bandits without individual arm feedback or linearity assumption.
result DART achieves a regret bound of i l d e O ( K K N T ) ilde{\mathcal{O}}(K\sqrt{KNT}) i l d e O ( K K N T ) . Paper proposes a novel SVM method for creating survival trees.
problem Creating non-linear survival trees for right-censored data.
method L2-regularized dipole splitting criteria with kernel methods.
result Non-linear splits using polynomial and Gaussian kernels show similar predictive power but often smaller tree sizes.
New algorithm tackles non-linear utility in MNL bandits with i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) regret.
problem Sequential assortment selection with intricate user-item interactions.
method Upper Confidence Bound principle for non-linear parametric utility functions, including neural networks.
result Achieves i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) regret bound for neural network-based utilities. Improved algorithm for logistic bandits with better regret bounds.
problem Understanding the impact of non-linearity in logistic bandits.
method Introducing a new algorithm and providing refined analysis.
result Improved regret bounds scaling as O ~ ( d T / κ ) \tilde{\mathcal{O}}(d\sqrt{T/κ}) O ~ ( d T / κ ) in most favorable cases. Master-slave architecture tackles combinatorial multi-armed bandits with diversity constraints.
problem Solving top- K K K combinatorial multi-armed bandits with non-linear feedback and diversity constraints. method Master-slave architecture with six slave models, teacher learning, and policy co-training.
result Significantly outperforms existing algorithms in synthetic and real datasets.
Improved regret bound for multinomial logistic bandits with non-linearity.
problem Maximizing rewards in multinomial logistic bandits with non-linear feedback.
method Extended the definition of κ ∗ κ_* κ ∗ to multinomial setting and proposed an efficient algorithm. result Minimax-optimal regret bound of O ~ ( R d K T / κ ∗ ) \smash{\widetilde{\mathcal{O}}( R d \sqrt{ {KT}/{κ_*}} ) } O ( R d K T / κ ∗ ) , improving over existing guarantees. New algorithm reduces linear contextual bandit regret with adversarial corruption.
problem Linear contextual bandit with adversarial reward corruption.
method Optimism in the face of uncertainty principle, weighted ridge regression.
result Achieves nearly optimal regret for both corrupted and uncorrupted cases.
New algorithms improve contextual bandits with neural networks and energy models.
problem Inefficient exploration in non-linear models for contextual bandits.
method Maximum entropy exploration using neural networks and energy models.
result Both techniques outperform standard algorithms, with energy models best overall.
Researchers compare different gradient methods for ridge regression, finding conjugate gradients have similar performance.
problem Comparing statistical properties of different gradient methods in ridge regression.
method Explicit non-standard error decomposition to bound prediction error of conjugate gradient iterates.
result Conjugate gradient iterates share optimality properties with gradient flow and ridge regression up to a constant factor.
Unified framework for multi-user bandits using Laplacian kernels.
problem Multi-user contextual bandits with graph-related users and non-linear rewards.
method Joint penalty combining graph smoothness and individual roughness in a unified RKHS.
result Unified multi-user RKHS and effective dimension for regret bounds.
Bayes-optimal learning of deep random networks with Gaussian weights is studied.
problem Learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights.
method Closed-form expressions for Bayes-optimal test error, ridge regression, kernel and random features regression are computed.
result Optimally regularized ridge regression and kernel regression achieve Bayes-optimal performances, while logistic loss yields a near-optimal test error for classification.
This paper studies semiparametric contextual bandits, a generalization of the linear stochastic bandit problem where the reward for an action is modeled as a linear function of known action features confounded by an non-linear action-independent term. We design new algorithms that achieve O ~ ( d T ) \tilde{O}(d\sqrt{T}) O ~ ( d T ) regret …
New algorithm achieves nearly optimal regret with one-pass updates for GLB problems.
problem Generalized linear bandits with non-linear reward distributions.
method Jointly efficient algorithm using OMD estimator with one-pass updates.
result Nearly optimal regret bound with O ( 1 ) \mathcal{O}(1) O ( 1 ) time and space complexities per round. A novel approach tackles sparse linear bandits with reduced communication costs and minimal cumulative regret.
problem Sparse linear bandits with high-dimensional feature vectors and limited relevant features.
method Cooperative Thresholded Lasso using Lasso and ridge regression for dimension reduction and aggregation.
result Regret bound of O ( s 0 log d + s 0 T ) \mathcal{O}(s_0 \log d + s_0 \sqrt{T}) O ( s 0 log d + s 0 T ) with high probability. New algorithms tackle RKHS bandits with reduced complexity and improved performance.
problem Adversarial and stochastic RKHS bandit problems with high computational complexity.
method Combining approximation theory with misspecified linear bandit methods.
result First general algorithm for adversarial RKHS bandit problem.
Paper introduces G-LowTESTR for efficient tensor bandits.
problem Efficient decision-making in multi-dimensional data with non-linear reward functions.
method Generalized low-rank tensor contextual bandits model and G-LowTESTR algorithm.
result G-LowTESTR achieves superior regret bound compared to vectorization and matricization methods.
We prove grokking in ridge regression, showing overfitting doesn't guarantee good generalization.
problem The onset of generalization long after overfitting in over-parameterized linear regression models.
method Proved end-to-end grokking results for learning over-parameterized linear regression models using gradient descent with weight decay.
result Generalization error eventually becomes arbitrarily small, but poor generalization persists long after overfitting.
Study contextual bandits with stage-wise constraints, proving regret bounds and extending results.
problem Contextual bandits with stage-wise constraints in high probability and expectation settings.
method Upper-confidence bound algorithms for linear and non-linear reward/cost functions, extending to multiple constraints.
result Regret bounds for various settings, including non-linear reward/cost functions.
Study on KRR with power-law data, showing better sample complexity.
problem High-dimensional kernel ridge regression with anisotropic power-law covariance.
method Explicit characterization of kernel spectrum and asymptotic analysis of excess risk.
result Sample complexity is governed by effective dimension, not ambient dimension.
Improved control approach for correlated bandits with better performance.
problem General multi-armed bandit problem with correlated elements.
method Introducing entropy regularisation to obtain a smooth asymptotic approximation of the value function, leading to a semi-index approximation of the optimal decision process.
result Performance of Asymptotic Randomised Control (ARC) algorithm compares favorably with other approaches.
Kernel-based function approximation improves reinforcement learning performance.
problem Average reward reinforcement learning in infinite horizon settings.
method Optimistic algorithm based on kernel ridge regression.
result No-regret performance guarantees and confidence intervals for kernel-based predictions.
Many real-world problems like Social Influence Maximization face the dilemma of choosing the best K K K out of N N N options at a given time instant. This setup can be modeled as a combinatorial bandit which chooses K K K out of N N N arms at each time, with an aim to achieve an efficient trade-off between exploration and expl…
INF-clip optimizes heavy-tailed MAB problems with improved performance.
problem Optimizing multi-armed bandit problems with heavy-tailed rewards.
method INF-clip algorithm for adversarial and stochastic heavy-tailed MAB settings.
result INF-clip is optimal for linear and non-linear heavy-tailed stochastic MAB problems.
GP-UCB resolves sublinear regret for kernelized bandits.
problem Minimizing regret in kernelized bandit problems.
method Using a new regularization technique for kernel ridge estimators, improving GP-UCB's sublinear regret rate.
result GP-UCB achieves nearly optimal sublinear regret for the Matérn kernel.
Kernelized bandit algorithm tackles adaptive contextual bandits with single-index models.
problem Adaptive contextual bandits with single-index models and unknown link functions.
method Kernelized ε-greedy algorithm combining Stein-based index estimation and kernel ridge regression for reward functions.
result Unified framework for simultaneous learning and inference in single-index contextual bandits.
We study two randomized algorithms for generalized linear bandits. The first, GLM-TSL, samples a generalized linear model (GLM) from the Laplace approximation to the posterior distribution. The second, GLM-FPL, fits a GLM to a randomly perturbed history of past rewards. We analyze both algorithms and derive $\tilde{O}(…
Proposes EE-Net for neural exploration in contextual bandits.
problem Exploitation-Exploration tradeoff in contextual bandits.
method Uses two neural networks: Exploitation and Exploration, to learn reward function and adaptively explore.
result Achieves O ( T log T ) \mathcal{O}(\sqrt{T\log T}) O ( T log T ) regret and outperforms existing methods. Oracle-efficient algorithms reduce combinatorial semi-bandit regret to logarithmic time.
problem Scalability issue in combinatorial semi-bandit problems due to high combinatorial optimization costs.
method Oracle-efficient frameworks that minimize oracle queries while maintaining tight regret guarantees.
result Achieved i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) regret with O ( log log T ) O(\log\log T) O ( log log T ) oracle queries for worst-case linear rewards. We study the regret minimization problem in the novel setting of generalized kernelized bandits (GKBs), where we optimize an unknown function f ∗ f^* f ∗ belonging to a reproducing kernel Hilbert space (RKHS) having access to samples generated by an exponential family (EF) reward model whose mean is a non-linear function $μ(…
Contextual multi-armed bandit problems arise frequently in important industrial applications. Existing solutions model the context either linearly, which enables uncertainty driven (principled) exploration, or non-linearly, by using epsilon-greedy exploration policies. Here we present a deep learning framework for cont…
A fair policy for hiring candidates from different groups is proposed in a linear contextual bandit problem.
problem Selecting candidates from different sensitive groups in a fair manner.
method A greedy policy that constructs a ridge regression estimate and computes relative rank using empirical cumulative distribution function.
result The greedy policy achieves fair pseudo-regret of order d T \sqrt{dT} d T after T T T rounds, satisfying demographic parity. A new algorithm for conversational recommendation systems using dueling bandits in GLMs.
problem Limited user feedback in existing conversational bandit methods.
method Integrates dueling bandits with relative feedback in generalized linear models.
result Theoretical and empirical validation of ConDuel's efficacy.
Efficiently performs robust and sparse kernel regression.
problem Robust and sparse kernel regression.
method Sign gradient descent and early stopping.
result Sign gradient descent achieves robust and sparse kernel regression efficiently.
Develops algorithms for CCBs with non-linear costs, improving safety and performance.
problem Safety constraints in sequential decision making with non-linear arm costs.
method Innovative algorithms using Inverse Gap Weighting (IGW) and online regression oracle.
result Sub-linear regret bounds for C-SquareCB and first-order regret for C-FastCB.
New algorithm reduces regret for logistic bandits without κ κ κ dependency.
problem Logistic bandits have poor frequentist regret guarantees due to large κ κ κ . method Optimistic algorithm based on self-normalized martingale tail-inequality.
result Achieves i l d e O ( T ) ilde{\mathcal{O}}(\sqrt{T}) i l d e O ( T ) regret with no κ κ κ dependency. Neural algorithms optimize arm selection with human preference feedback for complex reward functions.
problem Optimizing arm selection with noisy human preference feedback for complex, non-linear reward functions.
method Neural network to estimate reward function using preference feedback, upper confidence bound and Thompson sampling algorithms.
result Sub-linear regret guarantees for efficient arm selection in contextual dueling bandits.
SGD shows distinct phases in learning single-index models, achieving optimal sample complexity and regret.
problem Learning single-index models with SGD in adaptive data settings.
method Stochastic gradient descent (SGD) with an optimal learning rate schedule.
result SGD achieves near-optimal sample complexity and regret guarantees across both burn-in and learning phases.
We consider the task of robust non-linear regression in the presence of both inlier noise and outliers. Assuming that the unknown non-linear function belongs to a Reproducing Kernel Hilbert Space (RKHS), our goal is to estimate the set of the associated unknown parameters. Due to the presence of outliers, common techni…
New algorithm for differential private kernel bandits with improved regret bounds.
problem Contextual bandits with differential privacy constraints.
method Proposes a private kernel-ridge regression estimator using random projections.
result Achieves state-of-the-art cumulative regret bounds in both joint and local models of differential privacy.
This paper investigates how transformers can learn to generalize to unseen examples in context.
problem Understanding how transformers can generalize to unseen examples in a prompt.
method Gradient descent analysis of one-layer multi-head transformers for in-context learning.
result The training loss for a one-layer multi-head transformer converges linearly to a global minimum, effectively learning ridge regression over basis functions.
New algorithm catches moving subspaces in bandit problems.
problem Adapt to changing low-dimensional latent subspaces in bandit settings.
method Piecewise-stationary low-rank linear contextual bandits with CUSUM-style boundary detection.
result Achieves intrinsic rank dynamic regret rate of O ( r T ) O(r\sqrt{T}) O ( r T ) . A new estimator reduces variance in slate bandit OPE.
problem Large action spaces in slate bandits cause high variance in OPE.
method Develops Latent IPS (LIPS) to optimize slate abstractions for low variance and bias.
result LIPS substantially outperforms existing estimators in scenarios with non-linear rewards and large slate spaces.
Selecting important features in non-linear or kernel spaces is a difficult challenge in both classification and regression problems. When many of the features are irrelevant, kernel methods such as the support vector machine and kernel ridge regression can sometimes perform poorly. We propose weighting the features wit…
NeuralRBMLE tackles explore-exploit trade-offs in contextual bandits with neural networks.
problem Stochastic contextual bandit problem with general bounded reward functions.
method Reward-biased maximum likelihood estimation with neural networks to enforce exploration.
result Both NeuralRBMLE variants achieve O ~ ( T ) \widetilde{\mathcal{O}}(\sqrt{T}) O ( T ) regret.