Paper proposes a new adaptive multiscale value function approximation for reinforcement learning.
problem Value function approximation in reinforcement learning with varying complexity.
method Adaptive multiscale approximation using multiresolution analysis and tree approximation.
result Convergence rate of the multiscale approximation is independent of basis function regularity.
Study compares adaptive vs fixed query learning methods.
problem Comparing adaptive and fixed query learning methods for task approximation.
method Examined in-context and agentic learning in two settings: unrestricted and realizable.
result Adaptivity does not hinder performance in unrestricted setting but can in realizable setting.
Adaptive approximations improve variational inference for complex models.
problem Efficiently approximate marginal distributions and partition functions in complex probabilistic models.
method Two classes of adaptive approximations that include Bethe, tree-reweighted, and convex free energies.
result Proposed approximations automatically adapt to a given model and outperform existing methods.
New algorithm reduces interventional strategy complexity for causal graph discovery.
problem Designing efficient interventional strategies for causal graph discovery.
method Developed an r-adaptive algorithm for causal graph discovery that minimizes the number of interventions.
result Achieved an approximation of O(min{r, log n} * n^{1/min{r, log n}}) for the verification number.
Greedy policy achieves good results for adaptive submodular problems.
problem Sequential decision making with adaptive stochastic optimization.
method Adaptive submodularity ratio to analyze greedy policy performance.
result Greedy policy achieves approximation guarantees for a broader class of problems.
Adaptive neural network approximates stochastic system densities.
problem Approximating high-dimensional stochastic dynamical systems.
method Temporal KRnet (tKRnet) trained with adaptive collocation points and temporal decomposition.
result Improves density approximation for stochastic systems without curse of dimensionality.
New Hermite approximations accelerate convergence with adaptive coordinate transformations.
problem Accelerating convergence of spectral approximations for Hermite expansions.
method Using normalizing flows for adaptive coordinate transformations and deriving error estimates.
result Error estimates for Hermite expansions under adaptive coordinate transformations.
New guarantees for adaptive combinatorial maximization with various objectives.
problem Maximizing under cardinality constraints and minimum cost coverage in adaptive settings.
method Bayesian approach with comprehensive approximation guarantees for various utility functions.
result Maximal gain ratio is a new parameter that provides stronger approximation guarantees than greedy policies.
The paper analyzes stability in adaptive control systems with value iteration, considering approximation errors.
problem Stability of adaptive control systems during learning with approximation errors.
method Theoretical analysis of stability using value iteration, considering both constant and time-varying control policies.
result Estimations of the region of attraction to ensure function approximation remains valid.
Adaptive GMRA approximates high-dimensional data with low-dimensional geometric structures.
problem Efficiently approximating high-dimensional data from a nearly low-dimensional manifold.
method Adaptive GMRA with thresholding of geometric wavelet coefficients.
result Adaptive GMRA approximations perform well on various measures with different regularity.
Adaptive Gaussian process approximates Bayesian inference for costly likelihoods.
problem Bayesian inference with computationally expensive likelihood functions.
method Gaussian process approximation with active learning design points.
result Competitive performance compared to existing methods for Bayesian computation.
Paper tackles adaptive submodularity in sequential decision making.
problem Maximizing adaptive submodular functions with limited adaptive rounds.
method Proposes an efficient semi-adaptive policy with logarithmic adaptive rounds.
result Achieves an almost tight 1−1/e−ε approximation guarantee. Adaptive reduction scheme approximates optimal policy in regularized MDPs.
problem Finding near optimal policy in regularized MDPs with biased solutions.
method Adaptive reduction of regularization parameter λ to approximate optimal policy.
result Iteration complexity reduced for obtaining ε-optimal policy.
Neural networks learn adaptive kernels that improve approximation and representation.
problem Improving neural network performance in approximating and representing functions from data.
method Dynamic reproducing kernel Hilbert space (RKHS) approach.
result Gradient flow in neural networks learns an adaptive RKHS representation and performs global least-squares projection.
Fast algorithms developed for adaptive and fully adaptive submodular maximization problems.
problem Maximizing submodular functions subject to constraints in linear time.
method Developed linear-time algorithms for two submodular maximization problems: adaptive and fully adaptive.
result Achieved (1−1/e−ε) approximation ratio for adaptive submodular maximization and $ rac{1-1/e-ε}{4-2/e-2ε}$ for fully adaptive submodular maximization. New algorithm improves polynomial chaos approximations using compressive sensing.
problem Improving the efficiency and accuracy of polynomial chaos expansions.
method Develops a two-step optimization procedure combining compressive sensing with basis adaptation.
result Optimal sparsity in polynomial chaos approximations with reduced dimensionality.
Paper presents a Transformer model for automatic domain adaptation.
problem Challenges in selecting or designing domain adaptation algorithms.
method Transformer model approximates and selects domain adaptation algorithms.
result Transformers can approximate and automatically select domain adaptation algorithms.
Adaptive Nyström method improves Gaussian Process Regression scalability.
problem Scalability issue in Gaussian Process Regression due to cubic complexity.
method Adaptive Nyström approach that greedily selects landmarks to minimize kernel approximation error.
result Significantly outperforms random landmark selection in accuracy and stability.
New algorithm maximizes non-monotone adaptive submodular functions in linear time.
problem Maximizing non-monotone adaptive submodular functions subject to a cardinality constraint.
method Developed a linear-time algorithm for non-monotone adaptive submodular maximization.
result Achieved a 1/e−ε approximation ratio with O(nε−2logε−1) value oracle queries. Paper proposes adaptive control for unknown systems using reinforcement learning.
problem Adaptive control for unknown, linearizable systems.
method On-policy reinforcement learning for discrete-time, stochastic systems.
result Stability and tracking errors concentrate near zero with high probability.
A novel adaptive kernel improves RBF neural networks performance.
problem Improving performance of RBF neural networks.
method Adaptive fusion of Euclidean and cosine distance measures using gradient descent.
result The method outperforms manual fusion on three major problems.
New RL algorithm learns state aggregation architecture adaptively.
problem Adapting reinforcement learning value function architectures.
method Adapts state aggregation architecture using state visit frequency feedback.
result Improves RL performance on various test problems.
ADDA-KR uses KRnets for solving high-dimensional Fokker-Planck equations.
problem High-dimensional, unbounded Fokker-Planck equations.
method KRnet for density approximation, adaptive sampling for stochastic collocation.
result ADDA-KR efficiently approximates high-dimensional density functions.
LaLoRA prevents forgetting in LoRA fine-tuning.
problem Catastrophic forgetting in fine-tuned models.
method LaLoRA applies Laplace approximation to LoRA weights for regularization.
result Improved learning-forgetting trade-off with controllable regularization strength.
Deep networks adapt to function regularity and data distribution.
problem Understanding deep learning's adaptability to function regularity and data distribution.
method Developed nonparametric approximation and estimation theories for a broad class of functions using deep ReLU networks.
result Deep neural networks are adaptive to different regularity of functions and nonuniform data distributions.
Adapts reinforcement learning architectures using state visit frequency.
problem Determining an optimal approximation architecture for reinforcement learning.
method Adapts state aggregation approximation architecture based on state visit frequency.
result Guarantees VF estimate arbitrarily close to zero with large S. Adaptive Multilevel Monte Carlo improves probability estimation for complex random variables.
problem Estimating probabilities of complex random variables with multiple approximations.
method Adaptive Multilevel Monte Carlo framework for discontinuous functionals.
result Achieves optimal computational complexities for both smooth and discontinuous functionals.
Paper tackles adaptive sampling for identifying largest gaps between distributions.
problem Adaptive sampling from K distributions to identify the largest gap between any two adjacent means.
method Proposes elimination and UCB-style algorithms, showing minimax optimality.
result UCB-style algorithms require 6-8x fewer samples than non-adaptive sampling.
New MCMC algorithm reduces subset selection passes to 2 for optimal k-dimensional subspace approximation.
problem Subset selection for k-dimensional subspace approximation with ε-approximation. method MCMC sampling algorithm reducing passes to 2 for p=2 case, poly(k/ε) size subset. result Subset selection of nearly optimal size in 2 passes, (1+ε) approximation. Adapting functional gradients improves FGD's practicality and theoretical guarantees.
problem Implementing FGD in practice due to infinite-dimensional functional gradients.
method Adapting the representation of functional gradients.
result Establishes convergence to a stationary point for smooth losses and a global minimizer under smoothness + Polyak-Lojasiewicz condition.
AAPI improves regret bound for undiscounted continuing learning in uniformly ergodic MDPs.
problem Improving regret bounds for undiscounted continuing learning in uniformly ergodic MDPs.
method Adaptive approximate policy iteration (AAPI) with online learning techniques and data-dependent adaptive learning rate.
result AAPI achieves a ildeO(T2/3) regret bound, improving over the best existing bound of ildeO(T3/4). We analyze the computational limits of LoRA for transformer models using fine-grained complexity theory.
problem Computational efficiency of LoRA fine-tuning for transformer models.
method Fine-grained complexity theory, identifying phase transitions, almost linear algorithms.
result Existence of almost linear algorithms for LoRA adaptation based on specific norms.
Develops manifold calculus for simplicial complexes.
problem Approximating functors from simplicial complexes to topological spaces.
method Adapting manifold calculus to simplicial complexes and proving an approximation theorem.
result Functors can be approximated by polynomial functors under certain conditions.
New algorithms improve causal graph discovery with adaptive interventions, even under worst-case interventional costs.
problem Discover causal relationships from data with adaptive interventions and node-dependent costs.
method Define new benchmarks and provide adaptive search algorithms for causal graph discovery.
result Logarithmic approximations achieved under various settings: atomic, bounded size interventions and generalized cost objectives.
Unified framework for sampling and approximating high-dimensional energy landscapes.
problem Sampling and approximating complex energy landscapes in physical systems with constraints and energy barriers.
method Formulates a minimax optimization problem that jointly adapts surrogate approximation and adaptive sampling.
result Demonstrates effectiveness in biomolecular systems with up to 30 collective variables.
Big batch SGD improves optimization by growing batch sizes to maintain accurate gradients.
problem Noisy gradients in classical SGD make adaptive stepsize selection and automatic stopping difficult.
method Adaptive batch size growth to maintain a constant signal-to-noise ratio in gradient approximations.
result Similar convergence rates to classical SGD, automated learning rate selection possible.
TAGCN improves graph CNN performance without approximation.
problem Performance loss in spectral graph convolutional neural networks.
method Topology adaptive graph convolutional network (TAGCN) with adaptive filters.
result TAGCN outperforms existing spectral CNNs on various datasets.
Improved multilevel scheme for value-at-risk computation.
problem Discontinuity in Heaviside function affects value-at-risk computation.
method Adaptive multilevel stochastic approximation to mitigate discontinuity.
result Best complexity improved to O(ε−2∣lnε∣25). Paper proposes SRA algorithm for online learning robustness and adaptivity.
problem Quantifying and evaluating tradeoff between robustness and adaptivity in online learning.
method SRA algorithm using biased stochastic approximation scheme with adaptive threshold.
result SRA algorithm provides superior performance in synthetic and real datasets.
LoRA enhances model adaptability without increasing parameters.
problem Theoretical understanding of LoRA's adaptability.
method Theoretical analysis of LoRA's expressive power.
result LoRA can adapt any model to a smaller target model with a specific rank.
AIS algorithm improves heavy-tailed distribution estimation.
problem Inconsistent estimators and slow convergence in AIS for heavy-tailed distributions.
method Adapts Student-t proposal distributions by matching escort moments and minimizing α-divergence.
result Improves estimation accuracy for heavy-tailed distributions.
A framework isolates and learns approximately shared features for better domain adaptation.
problem Reducing performance degradation in unseen domains using machine learning models.
method Statistical framework distinguishing feature utilities based on correlation variance across domains. Learning approximately shared features from source tasks and fine-tuning on target tasks.
result Improved population risk compared to previous results on both source and target tasks, resolving the paradox of feature selection.
Adaptive learning rate algorithms such as RMSProp are widely used for training deep neural networks. RMSProp offers efficient training since it uses first order gradients to approximate Hessian-based preconditioning. However, since the first order gradients include noise caused by stochastic optimization, the approxima…
Adaptive algorithm speeds up k-nearest-neighbor searches.
problem Finding k nearest neighbors with varying efficiency.
method Adaptive estimation of distances to optimize search.
result The algorithm achieves significant speedups compared to naive methods.
Max-plus algebra approximates MDP value iteration for reduced state space.
problem Approximating optimal value function in high-dimensional MDPs.
method Uses max-plus algebra to represent value functions in a smaller dictionary, leading to an adaptive matching pursuit algorithm.
result Theoretical results show reduced complexity not tied to state space size, with empirical success on simple problems.
Study improves BN TTA under distribution shift using higher-order asymptotics.
problem Improving BN TTA for changing data distributions.
method Integrates Edgeworth expansion and saddlepoint approximation with one-step M-estimation.
result Derives optimal weighting parameter for minimized mean-squared error.
DALTON improves ODE parameter estimation by learning from noisy data.
problem High sensitivity to parameters in ODEs produces unreliable parameter estimates.
method Data-adaptive probabilistic likelihood approximation for ODEs.
result DALTON produces more accurate parameter estimates than existing methods.
Efficient RL algorithms for linear function approximation with limited adaptivity constraints.
problem Limited adaptivity in reinforcement learning with linear function approximation.
method Proposed two efficient online RL algorithms for episodic linear Markov decision processes under batch learning and rare policy switch models.
result Achieved efficient regret bounds for both batch learning and rare policy switch models, with substantial reduction in adaptivity.