This paper improves Bayesian optimization methods with tighter regret bounds and practical solutions.
problem Improving Bayesian optimization methods with tighter regret bounds and practical solutions.
method The paper analyzes and compares different acquisition functions (GP-UCB, TS, PIMS) to achieve tighter Bayesian cumulative regret bounds and address practical issues.
result PIMS achieves the tighter BCR bound and avoids hyperparameter tuning, unlike GP-UCB and TS.
New tighter confidence bounds for sequential kernel regression.
problem Quantifying uncertainty in sequential learning algorithms.
method Martingale tail inequalities and conic programming.
result New confidence bounds are tighter than existing ones.
New tighter bounds for learning algorithms from Steinke & Zakynthinou's supersample setting.
problem Improving generalization bounds for machine learning algorithms.
method Information-theoretic approach using projected loss and Rademacher sequence.
result The new bounds are tighter than previous information-theoretic bounds.
The standard interpretation of importance-weighted autoencoders is that they maximize a tighter lower bound on the marginal likelihood than the standard evidence lower bound. We give an alternate interpretation of this procedure: that it optimizes the standard variational lower bound, but using a more complex distribut…
Improved PAC-Bayesian bounds by considering example difficulty.
problem Improving generalization bounds in machine learning.
method Introducing a modified excess risk that leverages example difficulty to reduce variance and tighten PAC-Bayesian bounds.
result Tighter PAC-Bayesian generalization bounds for machine learning models.
A new method to measure neural network expressiveness using tighter upper bounds.
problem Measuring the expressiveness of deep neural networks (DNNs).
method Proposes a new tighter upper bound for the number of linear regions in rectifier networks, using matrix computation.
result The proposed upper bound is tighter than existing ones and explains the performance improvements of skip connections and residual structures.
Improved algorithm for online planning with tighter bounds.
problem Online planning in Markov Decision Processes with open-loop policies and budget constraints.
method Proposed KLOLOP algorithm with tighter upper-confidence bounds and efficient implementation.
result KLOLOP leads to better practical performances with sample complexity bound retained.
In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an information-theoretic setting, it is known that Fano's inequality typically doe…
New bound on generalization error using mutual information.
problem Generalization error in supervised learning.
method Information-theoretic bound on mutual information between samples and predictions.
result Tighter characterization of generalization error.
New tighter generalization bounds for deep networks like CNNs and ResNets.
problem Establishing tighter bounds for deep neural networks' generalization error.
method Introducing a new characterization of Lipschitz properties and margin-based data-dependent error bounds.
result Significantly tighter generalization bounds for deep neural networks, including CNNs and ResNets.
Improved median of means estimator with tighter bounds.
problem Improving the efficiency and reliability of median of means estimator.
method Modification of the median of means estimator with sub-Gaussian deviation bounds.
result Achieves nearly optimal constants under minimal assumptions.
Ahpatron improves online kernel learning with tighter mistake bounds.
problem Improving mistake bounds in online kernel learning with budget constraints.
method Introducing Ahpatron, a new model that uses an aggressive updating rule and a budget maintenance mechanism to approximate AVP.
result Ahpatron achieves tighter mistake bounds compared to previous models.
Proposes ETB for tighter bounds in robust training of deep networks.
problem Training robust deep neural networks to adversarial attacks.
method Proposes ETB, a provably tighter bound approach for interval bound propagation.
result Achieves orders of magnitudes tighter bounds compared to IBP.
Tighter ELBOs can harm learning, new algorithms improve performance.
problem Theoretical and empirical evidence shows that tighter ELBOs can reduce the signal-to-noise ratio of gradient estimators, hindering learning.
method Introduce three new algorithms: PIWAE, MIWAE, CIWAE, which improve over the standard IWAE.
result New algorithms can deliver improvements over IWAE, even when measured by IWAE's performance.
New RL algorithm gives tighter bounds without domain knowledge.
problem Improving worst-case performance bounds in reinforcement learning.
method Derives algorithm for finite horizon discrete MDPs with analysis yielding state-of-the-art worst-case regret bounds.
result Substantially tighter bounds for environments with small environmental norm, no prior knowledge required.
Improved bounds for Black-Scholes volatility lead to faster root-finding.
problem Finding accurate implied volatility for Black-Scholes model.
method Systematic use of option delta to derive tighter bounds, proposing a Newton-Raphson algorithm.
result Proposed algorithm converges rapidly for all price ranges, especially useful for extreme option prices.
Improved bounds on learning algorithms' performance using conditional mutual information.
problem Bounding the generalization error of learning algorithms.
method Introducing conditional mutual information and disintegrated mutual information to tighten bounds.
result New bounds are tighter than previous ones, especially for noisy, iterative algorithms.
The CUR matrix decomposition is an important extension of Nyström approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR algorithm with an expected relative-error bound. The proposed algorithm has the advanta…
The study tightens risk bounds for mixtures of experts using local differential privacy.
problem Improving risk bounds for mixtures of experts.
method Imposing local differential privacy (LDP) on the gating mechanism of mixtures of experts.
result Theoretical bounds exhibit logarithmic dependence on the number of experts and tighter than existing bounds.
Concentration inequalities are indispensable tools for studying the generalization capacity of learning models. Hoeffding's and McDiarmid's inequalities are commonly used, giving bounds independent of the data distribution. Although this makes them widely applicable, a drawback is that the bounds can be too loose in so…
Improved generalization bounds for SGD in non-convex learning.
problem Understanding generalization properties of SGD in non-convex settings.
method Introducing Type II perturbed SGD (T2pm-SGD) to analyze generalization error bounds.
result Tighter generalization error bounds for SGD in non-convex learning, especially for sub-Gaussian and bounded loss functions.
Improved algorithms for stochastic linear bandits using tighter confidence sequences.
problem Stochastic linear bandits with improved worst-case regret guarantees.
method Novel tail bound for adaptive martingale mixtures to construct tighter confidence sequences.
result Linear bandit algorithm achieves competitive worst-case regret.
New model generates graphs with tighter likelihood bounds and better quality.
problem Intractable likelihood of autoregressive graph models.
method Derive exact joint probability, approximate node orderings, variational inference.
result Lower bound on log-likelihood is significantly tighter than previous methods.
New bounds for CNNs show better generalization than previous models.
problem Improving understanding of CNNs' generalization ability.
method Proposed tighter generalization bounds for CNNs by exploiting the sparse and permutation structure of weight matrices and spectral norms of convolution operations.
result Theoretical and experimental results show tighter bounds for CNNs than existing bounds.
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.
The paper provides tighter error bounds for GPR under bounded support noise.
problem Rigorous error quantification for safety-critical applications with bounded noise.
method Using concentration inequalities and low complexity assumptions in RKHS, the paper derives probabilistic and deterministic error bounds for GPR.
result The derived error bounds are substantially tighter than existing state-of-the-art bounds and are particularly well-suited for GPR with neural network kernels.
Efficient local Lipschitz bounds improve neural network robustness.
problem Certifying robustness of neural networks is challenging and often leads to over-regularization.
method Proposes an efficient trainable local Lipschitz upper bound by considering activation functions and weight matrices.
result Consistently outperforms state-of-the-art methods in clean and certified accuracy on various datasets.
New bound for neural networks with full-rank weights, independent of network width.
problem Understanding generalization of neural networks with full-rank weight matrices.
method Using Koopman operators to derive a tighter generalization bound for full-rank weight matrices.
result The bound is tighter than existing norm-based bounds when condition numbers are small.
New algorithms reduce reinforcement learning regret in factored MDPs.
problem Optimizing reinforcement learning in non-episodic factored MDPs.
method Proposed two near-optimal and oracle-efficient algorithms for FMDPs.
result Oracle-efficient algorithms achieve near-optimal regret bounds of O ( D S A T ) O(DS\sqrt{AT}) O ( D S A T ) . PAC-Bayes with Backprop trains neural nets with competitive error estimates and tighter risk bounds.
problem Training probabilistic neural networks with PAC-Bayes bounds.
method Two training objectives derived from PAC-Bayes bounds, evaluated on MNIST and UCI data.
result Competitive test set error estimates and tighter risk bounds than previous results.
New bounds for SGD show improved performance in various settings.
problem Improving convergence bounds for SGD with random permutations.
method Analyzing convergence of SGD with random reshuffling and arbitrary permutations.
result Tighter lower bounds for weighted average iterates in both convex and strongly-convex cases.
Paper tightens variational GP approximations for large datasets.
problem Scaling Gaussian processes to large datasets.
method Relaxing the standard assumption about inducing points' posterior matching the prior, leading to a tighter variational approximation.
result The proposed approximation consistently matches or outperforms standard sparse variational GPs while maintaining computational cost.
New tighter lower bounds for DTW improve NN-DTW classification efficiency.
problem Efficient nearest neighbor search for DTW distances in time series.
method Developed new lower bounds leveraging DTW constraints for tighter and faster pruning.
result New lower bounds provide better balance between computation time and tightness.
A new framework tightens risk measure confidence bounds.
problem Improving confidence bounds for various risk measures.
method Distribution optimization framework with two estimation schemes based on concentration bounds.
result Consistently tighter confidence bounds compared to previous methods.
Algorithm identifies best arm with prior info in structured bandits.
problem Bayesian fixed-budget best-arm identification in structured bandits.
method Prior-dependent allocations based on structure and prior information.
result Improved theoretical bounds and robust performance across diverse models.
This work tightens generalization error bounds using Wasserstein distance.
problem Improving expected generalization error bounds in machine learning.
method Introduces bounds based on Wasserstein distance for various settings.
result New, tighter bounds based on relative entropy and other information measures.
Paper presents new training methods for neural networks with tighter risk certificates.
problem Training probabilistic neural networks with tighter risk certificates.
method Derived from PAC-Bayes bounds, two training objectives implemented for the first time in neural networks.
result Competitive test set errors and non-vacuous risk bounds with tighter values than previous results.
Improved Gaussian process regression with tighter log marginal likelihood bounds.
problem Improving predictive performance in Gaussian process regression models.
method Lower bound on log marginal likelihood using conjugate gradients.
result Improved predictive performance compared to other conjugate gradient based approaches.
Improved DP algorithms for non-convex optimization with tighter generalization bounds.
problem Private stochastic non-convex optimization in high-dimensional spaces.
method Differential privacy techniques, including adaptive algorithms like DP RMSProp and DP Adam, combined with adaptive data analysis.
result Achieved a sharper rate of p 4 / n \sqrt[4]{p}/\sqrt{n} 4 p / n for population loss, improving upon previous bounds. New PAC bound for meta-learning improves generalization guarantees.
problem Provide strong generalization guarantees in meta-learning.
method PAC-Bayes and uniform stability frameworks applied to gradient-based meta-learning.
result Derives a tighter PAC bound for gradient-based meta-learning.
We give bounds on the number of non-simple closed curves on a negatively curved surface, given upper bounds on both length and self-intersection number. In particular, it was previously known that the number of all closed curves of length at most L L L grows exponentially in L L L . We get exponentially tighter bounds given…
Combines chaining and mutual information methods for tighter generalization bounds.
problem Bounding generalization error of learning algorithms, especially in deep learning.
method Integrates chaining and mutual information methods to create a new generalization bound.
result Example shows significant improvement over existing bounds.
This work improves VAEs using MCMC methods for better variational bounds.
problem Improving the expressiveness of variational distributions in VAEs.
method Entropy-based adaptation for MALA/HMC chains to optimize tighter variational bounds.
result Higher held-out log-likelihoods and improved generative metrics.
Paper tightens PAC-Bayes bounds using coin-betting for better estimates.
problem Estimating mean of random elements with possibly S-dependent parameters.
method Refined PAC-Bayes proof strategy based on coin-betting framework.
result Derives tighter concentration inequalities for all sample sizes.
RAVEN-UCB addresses non-stationary MAB problems with tighter regret bounds.
problem Non-stationary environments in multi-armed bandits.
method Combines variance-aware adaptation with three innovations: confidence bounds, adaptive control, and recursive updates.
result Achieves tighter regret bounds than UCB1 and UCB-V.
Comparison results for rough and non-rough Heston models, tighter bounds on moment explosion times.
problem Comparing Heston models with and without roughness.
method Comparison principle for non-linear Volterra integral equations.
result Tighter bounds on moment explosion times for rough Heston models.
PopArt efficiently solves sparse linear bandits with tighter recovery guarantees.
problem Sparse linear bandits where rewards depend on a few covariates.
method PopArt: a simple, computationally efficient sparse linear estimation method.
result Improved regret bounds compared to state-of-the-art algorithms.
We provide bounds for kernel matrices and new approximations for high-dimensional data.
problem Approximating high-dimensional empirical kernel matrices.
method Decoupling results for U-statistics and non-commutative Khintchine inequality.
result New tighter approximations for inner-product kernel matrices.