Study improves self-normalized bounds for vector-valued processes beyond sub-Gaussianity.
problem Limited understanding of self-normalized concentration for vector-valued processes outside sub-Gaussian frameworks.
method Developed concentration inequalities for self-normalized processes with light tails (e.g., Bennett, Bernstein bounds) for vector-valued data.
result Provided new insights and bounds for self-normalized processes with non-sub-Gaussian distributions.
Tutorial on using concentration inequalities for linear system identification.
problem Learning state-space parameters of linear systems.
method Large-deviations and self-normalized martingales.
result Data-dependent and independent bounds on learning rate.
New bounds on self-normalized martingales improve online linear regression performance.
problem Improving regret bounds in online linear regression.
method Characterizing scale-invariant bounds on self-normalized martingales.
result For d = 1 d=1 d = 1 , O ( log T ) O(\log T) O ( log T ) doubly-uniform regret is possible; for d > 1 d>1 d > 1 , sublinear doubly-uniform regret is impossible. We improve bounds for stochastic processes, especially those with heavy tails.
problem Bounding the concentration of sub- ψ ψ ψ processes with heavy tails. method Variational approach to concentration, focusing on sub-Gaussian and other tail conditions.
result First dimension-free self-normalized empirical Bernstein inequality.
A new method for evaluating and selecting policies in contextual bandits improves confidence intervals and policy quality.
problem Evaluating and selecting policies in contextual bandits with logged data.
method Self-normalized Importance Weighting (SN) estimator with Efron-Stein tail inequality and multiplicative bias control.
result The method provides tighter confidence intervals and better policy selection compared to competitors.
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(…
New sampling method optimizes learning minimum mean among distributions.
problem Learning the minimum mean from a set of distributions.
method Developed Murphy Sampling, a novel approach.
result Murphy Sampling optimizes learning both low and high true minimums.
New inequalities for matrix supermartingales converge under various conditions.
problem Convergence and maximal inequalities of supermartingales in positive semidefinite matrices.
method Developed new concentration inequalities for matrix supermartingales.
result New inequalities for matrix supermartingales under different tail conditions.
New algorithms for contextual bandits with confounding effects achieve optimal regret.
problem Generalization of linear stochastic bandits with non-linear confounding effects.
method Design of new algorithms using a reward estimator inspired by doubly-robust approaches and new concentration inequalities for self-normalized martingales.
result Achieve i l d e O ( d T ) ilde{O}(d\sqrt{T}) i l d e O ( d T ) regret, matching best known bounds for unconfounded case and improving on recent results. Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently pro…
Adaptive kernel regression with streaming data and unknown variance.
problem Tackling adaptive regularization in streaming kernel regression with unknown noise variance.
method Generalized finite-dimensional linear regression to kernel setup, using self-normalized inequalities for variance estimation and adaptive regularization.
result Valid uniform bounds on mean function value at all points and time steps, leading to improved kernel bandit procedures.
Refines online learning to rank algorithm with tighter bounds.
problem Online learning to rank in machine learning.
method Utilized method of mixtures and asymptotic expansions to refine inequalities.
result Improved algorithm and performance estimation.
BR-SNIS reduces bias in self-normalized IS without increasing variance.
problem Bias in self-normalized IS.
method Iterated sampling-importance resampling (ISIR) to form a bias-reduced estimator.
result Significant reduction in bias without increasing variance.
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. Improved speech recognition with faster training and inference.
problem Training very deep CNNs for speech recognition is difficult.
method Proposed SNDCNN using SELU activations instead of RELU and shortcut connections/BN.
result Achieved similar or lower WER with faster training and inference.
A tutorial on non-asymptotic system identification methods.
problem Identifying system parameters in linear models.
method Covering technique, Hanson-Wright Inequality, method of self-normalized martingales.
result Streamlined proofs of least-squares based estimator performance.
The paper develops a method for self-normalized inference in adaptive experiments.
problem Adaptive experiments require a fixed horizon for ATE estimation, but propensities can change.
method The method uses self-normalized martingale limit theory to estimate ATE.
result The Studentized statistic is asymptotically N(0,1) at the prespecified horizon.
New algorithms reduce regret in neural logistic bandits.
problem Learning unknown reward functions in neural networks.
method Introduced a Bernstein-type inequality for self-normalized vector-valued martingales.
result Regret bounds improved to O ~ ( d ~ κ T ) \widetilde{O}(\widetilde{d}\sqrt{κT}) O ( d κ T ) and O ~ ( d ~ T / κ ) \widetilde{O}(\widetilde{d}\sqrt{T/κ}) O ( d T / κ ) . A new linear contextual bandit algorithm with improved regret bound.
problem Efficiently solving linear contextual bandit problems with reduced regret.
method Proposes a novel estimator embedded with exploration and a self-normalized bound.
result Regret bound matches lower bound of Ω ( d T ) Ω(\sqrt{dT}) Ω ( d T ) up to logarithmic factors. Self Normalizing Flows improve normalizing flows by reducing computational complexity.
problem Efficient gradient computation in normalizing flows, especially in Jacobian determinant terms.
method Introducing Self Normalizing Flows that replace expensive terms with learned approximate inverses.
result Models can be trained more quickly and perform better than functionally constrained counterparts.
New activation function SERLU improves neural network performance.
problem Improving neural network performance and avoiding overfitting.
method Introducing a new activation function (SERLU) that breaks monotonicity while preserving self-normalizing property and developing shift-dropout for regularization.
result SERLU-based neural networks provide consistently promising results compared to other activation functions.
Estimates stationary mass and frequency from non-i.i.d. data.
problem Estimating stationary mass and frequency from non-i.i.d. data.
method Combines plug-in estimator with WingIt modification for exponentially α α α -mixing processes. result Universal consistency in n n n for total variation distance estimation. Wavelet-based online learning adapts to noisy Besov spaces with high probability.
problem Minimizing integrated squared error in Besov spaces with noisy observations.
method Adaptive wavelet-based online learning algorithm that dynamically adjusts to gradient noise.
result Achieves minimax-optimal integrated squared error with high probability.
New algorithm reduces best-in-class regret in contextual bandits.
problem Compete with the best policy in a class without model restrictions.
method Proposes an algorithm that updates policies by minimizing a pessimistic objective, including a clipped inverse-propensity estimate and variance penalty.
result Achieves fast best-in-class regret rates, including polylogarithmic rates in the parametric case.
New algorithm learns policies without uniform overlap assumption.
problem Learning optimal policies from non-uniformly collected data.
method Pessimistic Policy Learning (PPL) using lower confidence bounds.
result Efficient policy learning for adaptively collected data.
Deep Learning has revolutionized vision via convolutional neural networks (CNNs) and natural language processing via recurrent neural networks (RNNs). However, success stories of Deep Learning with standard feed-forward neural networks (FNNs) are rare. FNNs that perform well are typically shallow and, therefore cannot …
Unified stopping rules ensure accurate policies in contextual learning.
problem Stopping data collection to ensure accurate policies in personalized decision problems.
method Developed unified stopping rules based on GLR statistics for pairwise action comparisons.
result Unified stopping rules achieve target precision with fewer samples than benchmarks.
Study tests adequacy of FARIMA models with uncorrelated but non-independent errors.
problem Testing adequacy of FARIMA models with specific error characteristics.
method Derive asymptotic distributions of residual autocovariances and autocorrelations, propose self-normalization approach.
result Asymptotic distributions of modified portmanteau statistics for weak FARIMA models.
The paper analyzes system identification with finite data.
problem Recovering system parameters and Kalman filter gain from noisy output measurements.
method Subspace identification algorithm, finite number of output samples, random matrix theory, self-normalized martingales, SVD robustness.
result Estimation errors decrease with a rate of 1/\sqrt{N}, valid even for marginally stable systems.
New RL algorithm for linear MDPs with nearly optimal regret.
problem Optimizing reinforcement learning for linear mixture Markov decision processes.
method Proposed a new Bernstein-type concentration inequality for self-normalized martingales and a computationally efficient algorithm UCRL-VTR+.
result UCRL-VTR+ achieves nearly minimax optimal regret of i l d e O ( d H T ) ilde O(dH\sqrt{T}) i l d e O ( d H T ) . New method improves feature importance assessment in random forests.
problem Improving feature importance measures for random forests.
method Hypothesis testing via self-normalized feature-residual correlation test (FACT).
result The method provides theoretically justified feature importance tests with controlled type I error and appealing power.
AMCI improves Monte Carlo integration by amortizing over both datasets and target functions.
problem Inefficiency in approximating expectations for known target functions using current approaches.
method Introduces AMCI, a method for amortizing Monte Carlo integration directly, producing three distinct amortized proposals.
result AMCI can theoretically produce arbitrarily small errors for any integrable target function using only a single sample from each proposal at runtime.
Paper controls false positives in high-dimensional models using a novel approach.
problem Controlling false positives in high-dimensional models with the Lasso.
method Recast SQRT-Lasso as a false positive control method, extend to all GLMs, use fast Lasso solvers.
result Shows novel false positive control using random weighted self-normalized sums in finite samples.
New algorithm reduces reinforcement learning regret for linear MDPs with unknown transitions.
problem Adversarial linear mixture MDPs with bandit feedback and unknown transition.
method Proposes a new algorithm with a least square estimator and self-normalized concentration.
result Achieves improved regret bound with high probability.
The stochastic multi-armed bandit model is a simple abstraction that has proven useful in many different contexts in statistics and machine learning. Whereas the achievable limit in terms of regret minimization is now well known, our aim is to contribute to a better understanding of the performance in terms of identify…
Finite-time queue peaks in stochastic networks have logarithmic scaling after geometric thresholds.
problem Queue peak laws in stochastic networks with geometric thresholds.
method Self-normalization mechanism
result Logarithmic scaling of queue peaks after geometric thresholds.
New algorithm reduces regret for linear bandits with unknown noise variance.
problem Finding optimal actions in linear bandits with varying noise variance.
method Adaptive algorithm with Freedman-type concentration inequality and multi-layer structure.
result Achieves i l d e O ( d ∑ k = 1 K σ k 2 + d ) ilde{O}(d \sqrt{\sum_{k = 1}^K σ_k^2} + d) i l d e O ( d ∑ k = 1 K σ k 2 + d ) regret for linear bandits. This paper develops dimension-agnostic inference methods for high-dimensional data.
problem Understanding how classical inference methods behave in high-dimensional settings.
method Using variational representations, sample splitting, and self-normalization to create a refined test statistic.
result The resulting statistic has a Gaussian limiting distribution regardless of how dimensionality scales with sample size.
Proposes SQUAD for better predictive uncertainty in deep latent models.
problem Intractable inference in deep latent variable models lead to overconfident predictions.
method Introduces Stochastic Quantized Activation Distributions (SQUAD) for flexible yet tractable latent variable distributions.
result The model provides competitive quality predictive uncertainty and learns non-linearities.
New bounds for estimating partition functions under bounded f-divergence.
problem Estimating partition functions with limited sample access.
method Information-theoretic characterization using integrated coverage profile and f f f -divergences. result Sharp phase transitions in sample complexity under f f f -divergences. New framework for evaluating ad auctions using stochastic modeling.
problem Challenges in evaluating deterministic ad auctions.
method Repurposed bid landscape model to approximate propensity scores, enabling robust OPE estimators.
result Remarkable alignment with online A/B test results, achieving 92% MDA in CTR prediction.
The paper proposes a method for constructing confidence sets that adapt to the cardinality of the smallest component of a mean vector.
problem Forming confidence sets for the smallest component of an unknown mean vector.
method Sample splitting and self-normalization approach to test each component for being the smallest, maintaining validity regardless of d d d and n n n . result The proposed tests achieve the local minimax separation rate and robust to heavy-tailed distributions.
New algorithm tackles heavy-tailed rewards in RL with instance-dependent regret bounds.
problem Efficient algorithms for RL with heavy-tailed rewards in large state-action spaces.
method Design of \textsc{Heavy-OFUL} for heavy-tailed linear bandits and \textsc{Heavy-LSVI-UCB} for RL with linear function approximation.
result First instance-dependent regret bounds for heavy-tailed rewards in RL with linear function approximation.
Optimizes assortment decisions with a new OFU scheme for online choice problems.
problem Online assortment optimization under stochastic choice with revenue performance and inference quality considerations.
method Forced-exploration OFU scheme combining regularized estimators for decision making and inference.
result Explicit regret bound and error bounds for approximate optimistic actions, showing Pareto optimality.
A new aggregation strategy improves GNN performance and learning dynamics.
problem Improving expressivity and learning dynamics of GNNs.
method Proposes a variance-preserving aggregation function (VPA) for GNNs.
result VPA leads to increased predictive performance and improved learning dynamics.
The study reveals the efficiency of sampling from tilted distributions.
problem Sampling from a tilted distribution of an unknown underlying distribution.
method Self-normalized importance sampling to characterize accuracy.
result Polynomial vs super-polynomial sample complexity for bounded vs unbounded distributions.
Cost-aware SBI reduces expensive simulations in complex models.
problem High computational cost in simulating complex models.
method Combination of rejection and self-normalised importance sampling.
result Significant reduction in overall cost of inference.
We develop a probabilistic framework for sequential random projection.
problem Challenges of sequential decision-making under uncertainty.
method Novel construction of a stopped process and method of mixtures.
result Achieved a non-asymptotic probability bound for random projection.