Adjoint sampler targets infinite-dimensional function spaces for efficient sampling.
problem Limited theory and algorithms for sampling infinite-dimensional function spaces.
method Adjoint Sampler for infinite-dimensional function spaces based on stochastic maximum principle.
result FAS achieves superior performance in synthetic and real systems.
Extended elliptical slice sampling for infinite-dimensional spaces, proving reversibility.
problem Proving reversibility of elliptical slice sampling in infinite-dimensional spaces.
method Extended elliptical slice sampling to infinite-dimensional separable Hilbert spaces, providing an alternative proof of reversibility.
result The approach yields a positive semi-definite Markov operator, proving reversibility.
The paper extends Thompson Sampling to infinite action spaces using information theory.
problem Addressing the limitation of finite action spaces in Thompson Sampling.
method Information-theoretic analysis, extending rate-distortion theory to infinite action spaces.
result Derives a near-optimal regret bound for bandits with infinite and continuous action spaces.
Improved multi-group learning with group-realizable concepts.
problem Enhancing multi-group learning efficiency.
method Empirical risk minimization over group-realizable concepts.
result Improved sample complexity in group-realizable settings.
Unified meta algorithms estimate various distribution functionals in infinite-armed bandits.
problem Estimating various distribution functionals in infinite-armed bandits.
method Unified meta algorithms for offline and online settings, achieving optimal sample complexities.
result Online estimation offers significant advantage for certain distribution functionals.
New findings on depth vs. width in neural networks, showing depth can improve learnability.
problem Understanding the role of depth in neural networks, especially when width is unbounded.
method Analyzing sample complexity for learnability in norm-controlled depth-2 and depth-3 ReLU networks.
result Depth can improve learnability of functions that are otherwise unlearnable with depth-2 networks.
New method reduces infinite variance in probabilistic programs with rejection sampling.
problem Infinite variance in naive importance sampling for programs with rejection sampling.
method Developed a new amortized importance sampling estimator with finite variance proof.
result Empirically demonstrated efficiency and correctness compared to existing alternatives.
We extend diffusion models to function spaces and introduce a new method for sampling from posterior distributions.
problem Sampling from posterior distributions in infinite-dimensional function spaces using diffusion models.
method Infinite-dimensional extension of Doob's h h h -transform, Supervised Guidance Training for efficient sampling. result We prove that diffusion models can be conditioned to sample from posterior distributions and introduce a simulation-free score matching objective.
Derives PF-ODE for infinite-dimensional functions, improving function generation tasks.
problem Efficient inference in infinite-dimensional diffusion models.
method Derives PF-ODE in infinite-dimensional function spaces.
result Reduces function evaluations while maintaining sample quality.
Bayesian algorithms improve online learning with adversaries over infinite action spaces.
problem Online learning with adversaries over infinite action spaces.
method Developed a Thompson sampling algorithm for online learning with an adversary's prior over the space of actions.
result Thompson sampling over a Gaussian process prior achieves a rate of O ( β T d log ( 1 + d λ β ) ) O(β\sqrt{Td\log(1+\sqrt{d}\fracλβ)}) O ( β T d log ( 1 + d β λ ) ) against a β β β -bounded λ λ λ -Lipschitz adversary. Optimal algorithm for selecting high-quality arms from infinite bandit arms.
problem Efficiently choosing the best arm from an infinite set of options.
method Developed algorithms for both fixed confidence and fixed budget settings, achieving optimal or near-optimal sample complexities.
result Optimal sample complexity results for both fixed confidence and fixed budget settings, resolving open questions in the field.
Paper investigates optimal transport map estimation in infinite-dimensional spaces.
problem Estimating optimal transport maps in infinite-dimensional spaces is challenging.
method Characterizes γ γ γ -smoothness for optimal transport maps and develops a polynomial-rate estimator. result Shows polynomial-order minimax risk for optimal transport map estimation.
Recurrent models can produce infinite sequences, causing bias; new methods prevent this.
problem Inconsistency in decoding infinite-length sequences from recurrent language models.
method Defined and proved inconsistency of common decoding algorithms; proposed remedies.
result Proposed methods prevent inconsistency in practice.
The paper analyzes the sample complexity of offline RL with linear approximations, identifying a hard regime and providing an algorithm.
problem Sample complexity of policy evaluation in infinite-horizon offline reinforcement learning with linear function approximation.
method Identification of a hard regime and construction of hard instances; algorithm with sample complexity bound.
result An algorithm that guarantees approximation to the value function up to an additive error of ε with high probability.
Study of linear classifiers in infinite imbalance scenarios.
problem Behavior of linear discriminant functions in extreme imbalance conditions.
method Analysis of linear classifiers under infinite imbalance, focusing on weight function properties and limit behavior.
result Limiting coefficient vectors reflect robustness or conservatism, optimizing against worst-case alternatives.
New method for Bayesian inference in infinite dimensions using SDMs.
problem Bayesian inference in infinite-dimensional function spaces.
method Amortized conditional score-based diffusion models (SDMs).
result Validated approach for large-scale, discretization-invariant Bayesian inference.
Paper improves reinforcement learning efficiency with deterministic value gradients.
problem High sample complexity in model-free DDPG algorithms for continuous control tasks.
method Proposes DVG and DVPG algorithms with infinite horizon value gradients to improve sample efficiency.
result DVPG algorithm substantially outperforms state-of-the-art methods on continuous control benchmarks.
Neural operators learn to solve LQ MFGs efficiently in infinite dimensions.
problem Solving many related LQ MFG problems in infinite-dimensional settings.
method Training neural operators to map problem data to equilibrium strategies.
result NOs reliably solve unseen LQ MFG variants with controlled parameters.
This paper improves Thompson Sampling for complex decision-making problems.
problem Learning in infinite-horizon discounted decision processes with unknown parameters.
method Developed a general canonical probability space and new metrics for analyzing adaptive learning algorithms.
result Thompson Sampling achieves complete learning in complex decision-making problems.
We consider the problem of near-optimal arm identification in the fixed confidence setting of the infinitely armed bandit problem when nothing is known about the arm reservoir distribution. We (1) introduce a PAC-like framework within which to derive and cast results; (2) derive a sample complexity lower bound for near…
Infinite Hidden Markov Models (iHMM's) are an attractive, nonparametric generalization of the classical Hidden Markov Model which can automatically infer the number of hidden states in the system. However, due to the infinite-dimensional nature of transition dynamics performing inference in the iHMM is difficult. In th…
Alexander method extended to infinite-type surfaces.
problem Determining equality of elements in mapping class groups.
method Combinatorial tool extended to infinite-type surfaces.
result Verification of relations and triviality of centers in mapping class groups.
Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is diffuse and it is hard to interpret the sampled partitionings. In this paper, we…
This paper shows how infinitely wide Tensor Networks converge to Gaussian Processes.
problem Understanding the relationship between Tensor Networks and Gaussian Processes.
method Analyzing the infinite-width limit of Tensor Networks and comparing them to Gaussian Processes.
result Infinitely wide Tensor Networks converge to Gaussian Processes, proving their equivalence.
UCoS avoids forward model evaluations in sampling for large-scale linear inverse problems.
problem Efficient sampling from posterior distributions in large-scale linear inverse problems.
method UCoS approach that learns a task-dependent score function offline and uses affine transformations to derive the conditional score.
result UCoS eliminates the need for forward model evaluations during sampling, making it more efficient.
An infinite parallel tempering bouncy particle sampler improves sampling efficiency for multimodal distributions.
problem Sampling from complex posterior distributions with high accuracy and efficiency.
method Introduced an infinite parallel tempering bouncy particle sampler (BPS-PT) to accelerate convergence.
result Demonstrated improved sampling efficiency for multimodal distributions through numerical simulations.
Study evaluates initialization strategies for infinite hidden Markov models.
problem Limited attention to initialization in infinite hidden Markov models.
method Systematically evaluated distance-based clustering, model-based, and uniform initializations.
result Distance-based clustering initializations consistently outperform other methods.
The study reveals a transition in neural network performance from infinite-width to variance-limited behavior as dataset size increases.
problem Understanding the transition from infinite-width to variance-limited behavior in neural networks.
method Empirical study of the transition from infinite-width to variance-limited behavior as a function of sample size and network width.
result The critical sample size \( P^* \) is approximately \( \sqrt{N} \) for polynomial regression with ReLU networks.
New framework allows reinforcement learning with polynomial sample complexity.
problem Generalization in reinforcement learning with function approximation.
method Introduces Bilinear Classes, a structural framework for RL.
result Polynomial sample complexity for Bilinear Classes, matching best known bounds.
Transformers capture combinatorial tasks with bounded error and logarithmic sample dependence.
problem Capturing complex combinatorial tasks with bounded error and sample efficiency.
method Formal definition of algorithmic capture, empirical analysis of infinite-width transformers, upper bounds on computational complexity.
result Transformers exhibit an inductive bias favoring simpler algorithmic procedures over higher complexity ones.
This short note aims at (re)proving that the symmetrically normalized graph Laplacian $L=\Id - D^{-1/2}WD^{-1/2}$ (from a graph defined from a Gaussian weighting kernel on a sampled smooth manifold) converges towards the continuous Manifold Laplacian when the sampling become infinitely dense. The convergence rate with …
A fundamental question in reinforcement learning is whether model-free algorithms are sample efficient. Recently, Jin et al. \cite{jin2018q} proposed a Q-learning algorithm with UCB exploration policy, and proved it has nearly optimal regret bound for finite-horizon episodic MDP. In this paper, we adapt Q-learning with…
New algorithm improves inference for flexible models with infinite latent features.
problem Inference for models with infinite latent features is computationally challenging and limiting.
method Adaptive slice sampling for posterior inference with general completely random measures.
result Higher effective sample size and predictive performance compared to existing methods.
Infinite-dimensional diffusion models tackle generative tasks for complex data.
problem Challenges in applying diffusion models to infinite-dimensional data.
method Directly formulate diffusion-based generative models in infinite dimensions.
result Developed guidelines for designing infinite-dimensional diffusion models.
New method reduces over-parametrization in neural networks, ensuring sparsity and finite network size.
problem Over-parametrization leads to too many active neurons in neural networks, especially with large data.
method Investigates a nonconvex regularization method for shallow ReLU networks.
result Locally optimal networks are finite even with infinite data, maintaining approximation guarantees and network size bounds.
Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as Diffusion Maps and Laplacian Eigenmaps are often used for manifold learning and non-linear dimensionality reduction. It was previously shown by Belkin and Niyogi \cite{belkin_niyogi:2007} that the eigenvectors and eige…
This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process, the mixture model has the advantages of modeling multimodal data and alleviating…
Sum-of-norms clustering recovers mixtures of Gaussians even with infinite samples.
problem Recovering a mixture of Gaussians from a large number of samples.
method Sum-of-norms clustering with equal weights, convex optimization.
result Sum-of-norms clustering can recover mixtures of Gaussians even as the number of samples tends to infinity.
Infinite width ReLU networks can approximate functions with bounded Euclidean norm.
problem Functions that can be approximated by ReLU networks with bounded Euclidean norm.
method Analyzing the minimal network norm required to approximate a given function.
result The minimal network norm for representing a function \( f \) is \( \max(\int |f''(x)| dx, |f'(-\infty) + f'(+\infty)|) \).
This paper improves sample complexity for AC and NAC algorithms under Markovian sampling.
problem Improving sample complexity for actor-critic and natural actor-critic algorithms.
method Characterizes convergence rate and sample complexity under Markovian sampling and mini-batch data.
result Improves sample complexity for AC and NAC algorithms by orders of magnitude.
Improved RL algorithm with linear MDPs for offline learning with partial data coverage.
problem Efficient offline RL with linear MDPs under partial data coverage.
method Primal-dual algorithm with O ( ε − 2 ) O(ε^{-2}) O ( ε − 2 ) sample complexity. result First computationally efficient algorithm with O ( ε − 2 ) O(ε^{-2}) O ( ε − 2 ) sample complexity for offline RL with linear MDPs under partial data coverage. Thompson Sampling reduces regret in non-episodic restless bandits.
problem Learning optimal policies in time-varying reward systems.
method Variant of Thompson Sampling applied to infinite horizon restless bandits.
result Sub-linear regret bound of O ( T log T ) O(\sqrt{T}\log T) O ( T log T ) proved for non-episodic case. Paper reduces variance in infinite horizon off-policy evaluation with bias reduction.
problem High variance in infinite horizon off-policy evaluation.
method Doubly robust augmentation of Liu et al. (2018a) method using learned value function.
result Significant reduction in bias with higher accuracy when either density ratio or value function is accurate.
Method solves Bayesian inverse problems in function space without assuming log-concavity.
problem Bayesian inverse problems in infinite-dimensional nonlinear settings.
method Score-based diffusion models as a prior, Langevin-type MCMC on function spaces.
result Provable convergence bound for posterior sampling, dependent on score approximation.
Proposes pT-Learning for optimal dynamic treatment regimes in mHealth.
problem Challenges in learning optimal dynamic treatment regimes with large intervention options and infinite time horizon.
method Proximal Temporal consistency Learning (pT-Learning) framework for adaptively adjusting between deterministic and stochastic policies.
result Minimax estimator avoids double sampling issue and can incorporate off-policy data.
Paper overcomes sample size barrier in reinforcement learning with generative models.
problem Sample efficiency in reinforcement learning with generative models.
method Developed two algorithms to certify minimax optimality of sample complexity.
result Achieved minimax-optimal guarantees for a wide range of sample sizes.
This paper proves neural networks can approximate any infinite-dimensional map with uniform guarantees.
problem Universal approximation of infinite-dimensional maps by neural networks with uniform guarantees.
method Analysis of various infinite analogues of neural networks and their approximation capabilities.
result Any continuous map can be approximated arbitrarily closely by some infinite neural networks with mild topological conditions.
Directional and pairwise measurements are often used to model inter-relationships in a social network setting. The Mixed-Membership Stochastic Blockmodel (MMSB) was a seminal work in this area, and many of its capabilities were extended since then. In this paper, we propose the \emph{Dynamic Infinite Mixed-Membership s…