Wide neural networks can learn complex functions like gravitational force law.
problem Learning complex functions like gravitational force law with neural networks.
method Extending theoretical bounds to analytic functions on the sphere using SGD and ReLU networks.
result Wide ReLU networks can learn analytic functions efficiently with proportional number of samples.
Greedy method adds neurons one by one for better function approximation.
problem Function approximation in neural networks.
method Growing deep neural network by adding one neuron at a time with non-linear activation.
result Accurate approximants for model problems in function approximation.
In this work, we study value function approximation in reinforcement learning (RL) problems with high dimensional state or action spaces via a generalized version of representation policy iteration (RPI). We consider the limitations of proto-value functions (PVFs) at accurately approximating the value function in low d…
New approach to bilevel optimization for machine learning using functional methods.
problem Solving bilevel optimization problems in machine learning, especially with over-parameterized neural networks.
method Functional point of view, scalable and efficient algorithms for functional bilevel optimization.
result Demonstrates benefits of functional approach on instrumental regression and reinforcement learning tasks.
When fitting Bayesian machine learning models on scarce data, the main challenge is to obtain suitable prior knowledge and encode it into the model. Recent advances in meta-learning offer powerful methods for extracting such prior knowledge from data acquired in related tasks. When it comes to meta-learning in Gaussian…
Paper introduces a new curriculum generation method for reinforcement learning.
problem Improving reinforcement learning performance and speed through curriculum learning.
method The paper proposes a novel curriculum generation paradigm based on progression and mapping functions.
result Empirical results show the new approach outperforms state-of-the-art algorithms.
Deep RBVFs improve continuous control in RL.
problem Challenges in finding optimal actions for continuous actions in RL.
method Introduced deep radial-basis value functions (RBVFs) for continuous control.
result RBF-DQN significantly outperforms value-function-only baselines and is competitive with actor-critic algorithms.
Develops methods to measure and set function-space learning rates in neural networks.
problem Measuring and optimizing changes in neural network output functions.
method Efficient methods to measure and set function-space learning rates, requiring minimal computational overhead.
result Demonstrates FLeRM (Function-space Learning Rate Matching) for hyperparameter transfer across model scales.
A new algorithm for learning from functional data across multiple machines.
problem Handling large-scale functional data analysis.
method Distributed Gradient Descent Functional Learning (DGDFL) algorithm.
result First theoretical understanding and optimal learning rates for DGDFL.
A new method for functional data classification using supervised manifold learning.
problem Improving classification of functional data.
method Supervised manifold learning approach considering label information.
result The proposed method achieves highly competitive performance compared to existing methods.
Survey on learning Boolean functions in computational theory.
problem Learning Boolean function classes in computational theory.
method Overview of known results in PAC and related models.
result Discussion of various learning results for Boolean functions.
Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if t…
MetaFun learns functional representations for meta-learning.
problem Few-shot classification on large-scale datasets.
method Functional encoder-decoder approach with iterative updates.
result State-of-the-art performance on miniImageNet and tieredImageNet.
Efficient offline reinforcement learning with neural networks using differentiable function approximation.
problem Statistical efficiency of offline reinforcement learning with function approximators.
method Pessimistic fitted Q-learning (PFQL) and differentiable function approximation.
result Provably efficient offline reinforcement learning with differentiable function approximation.
New algorithm learns value and advantage functions for continuous-time Markov processes without structural assumptions.
problem Learning value and advantage functions for continuous-time Markov processes without structural assumptions.
method Proposes Sobolev-prox fitted q-learning algorithm based on Hilbert-space positive definiteness and boundedness properties of Bellman operators. result Identifies ellipticity as a key structural property enabling reinforcement learning for Markov diffusions.
VIABLE learns a loss function for better few-shot learning.
problem Few-shot learning underfits with standard loss functions.
method Meta-learning to learn a differentiable loss function.
result Learning a relational loss function improves performance and sample efficiency.
In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of reproducing kernel Hilbert space theory to learn from such functional data. Basi…
Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns linear factored functions (LFF). This class of functions has structural properties …
Continuous-time Q-learning theory developed for reinforcement learning.
problem Continuous-time reinforcement learning challenges.
method Entropy-regularized, exploratory diffusion process formulation; first-order approximation of Q-function; martingale conditions.
result Developed a q-learning theory independent of time discretization.
New method learns neural network activation functions from data.
problem Learning activation functions for neural networks.
method Model each neuron's activation function as a small neural network.
result Learned activation functions improve network performance.
Proposes a neural network autoencoder for smoothing and representation learning of functional data.
problem Lack of sufficient nonlinear representations in existing methods for functional data analysis.
method Develops a neural network autoencoder architecture to process functional data directly, learning both smoothing and representation.
result Outperforms traditional methods in prediction, classification, and computational efficiency.
Q-learning with function approximation is one of the most popular methods in reinforcement learning. Though the idea of using function approximation was proposed at least 60 years ago, even in the simplest setup, i.e, approximating Q-functions with linear functions, it is still an open problem on how to design a pr…
Adaptive neural networks learn functional data bases for improved performance.
problem Applying deep learning to functional data is challenging due to high dimensionality.
method Proposes adaptive neural networks with Basis Layers that learn relevant basis functions.
result Empirically outperforms other neural network approaches across various tasks.
Improves imitation learning in RL by learning reward function efficiently.
problem Lack of effective reward function approximation in AIRL for imitation tasks.
method Proposes Off-Policy AIRL that combines adversarial learning with efficient reward function approximation.
result Shows superior imitation performance and efficiency compared to state-of-the-art AIL algorithms.
Paper proposes a new loss function for PU learning without negative examples.
problem Traditional machine learning struggles with negative examples, leading to biased predictions.
method Developed a collective loss function (cPU) for positive and unlabeled data.
result The cPU consistently outperforms existing methods in PU learning benchmarks and real-world datasets.
m-arcsinh improves SVM and MLP reliability and speed in scikit-learn.
problem Improving SVM and MLP reliability and speed in scikit-learn.
method Modified arcsinh function for kernel and activation in SVM and MLP.
result Competitive classification performance and reliability of SVM and MLP with m-arcsinh.
Automatically discovers effective activation functions for deep learning.
problem Inconsistent performance of novel activation functions in deep learning networks.
method Evolutionary search for general form, gradient descent for parameters.
result Significant performance improvements over ReLU and other functions.
RI-DeepONet learns neural operators from arbitrary sensor data.
problem Discretization of input functions limits practical applications of DeepONet.
method Introduces RI-DeepONet and two dictionary learning algorithms for INRs.
result RINO handles arbitrary sensor data robustly and applies to various problems.
Develops hierarchical reinforcement learning value function approximators.
problem Estimating long-term returns in reinforcement learning with multiple goals.
method Introduces hierarchical universal value function approximators (H-UVFAs) using the options framework.
result Demonstrates generalization and improved performance of H-UVFAs over UVFAs.
New neural network models learn symmetric functions of varying input sizes.
problem Learning symmetric functions with varying input sizes.
method Functional perspective on neural networks, treating symmetric functions as functions over probability measures.
result Established approximation and generalization bounds for shallow architectures that extend across input sizes.
This paper connects functional data analysis with machine learning techniques.
problem Lack of theoretical analysis for functional depths.
method Viewing functional depths as kernel mean embeddings in machine learning.
result Facilitates answers to open questions about functional depths.
New framework estimates target functions from incomplete data.
problem Estimating target functions from partially observed data.
method IF-learning framework using influence functions.
result Two learning algorithms developed for estimation.
New algorithms improve distributional TD learning with linear approximations.
problem Estimating return distributions in reinforcement learning.
method Fine-grained analysis of linear-categorical Bellman equation, variance reduction techniques.
result Tight sample complexity bounds for distributional TD learning with linear approximations.
An appropriate choice of the activation function (like ReLU, sigmoid or swish) plays an important role in the performance of (deep) multilayer perceptrons (MLP) for classification and regression learning. Prototype-based classification learning methods like (generalized) learning vector quantization (GLVQ) are powerful…
New algorithms learn sparse set functions in non-orthogonal Fourier bases.
problem Learning sparse set functions in non-orthogonal Fourier bases.
method Novel algorithms using non-orthogonal Fourier transforms.
result At most nk−klog2k+k queries for k non-zero Fourier coefficients. This paper proposes a new global optimization algorithm using deep learning.
problem Developing efficient algorithms for global optimization of non-convex functions.
method Two-phase approach: minimization phase with model-driven deep learning, escaping phase with reinforcement learning.
result The proposed algorithm significantly outperforms classical optimization methods and handles ill-posed functions.
Proposes a method to learn both constraints and objective functions from data.
problem Data-driven inverse optimization for mixed-integer linear programs (MILPs).
method Two-stage approach: first learns constraints, then estimates objective-function weights conditioned on learned constraints.
result Proposes and validates a method for learning both objective functions and constraints from data.
The paper explores transferring functions from one data space to another.
problem Approximating a function on a new data set using a learned function from an old data set.
method Transfer learning from one data space to another, focusing on subsets of the target data space.
result Local smoothness of the function and its lifting are related.
In reinforcement learning, Return, which is the weighted accumulated future rewards, and Value, which is the expected return, serve as the objective that guides the learning of the policy. In classic RL, return is defined as the exponentially discounted sum of future rewards. One key insight is that there could be many…
Study nonparametric covariance function estimation for noisy data.
problem Estimating covariance function from discrete noisy data in high dimensions.
method Adaptive learning-based estimators, including deep learning.
result Established oracle inequality and convergence rates for deep learning estimators.
Temporal difference methods enable efficient estimation of value functions in reinforcement learning in an incremental fashion, and are of broader interest because they correspond learning as observed in biological systems. Standard value functions correspond to the expected value of a sum of discounted returns. While …
Boosts Q-learning by using value function bounds.
problem Efficiently solving new tasks using past experience.
method Derives double-sided bounds on optimal value function and uses them to update Q-function.
result Boosted training performance through alternative Q-function update method.
A new framework learns system design using neural features in function space.
problem Learning system design with neural feature extractors.
method Introduces feature geometry in function space, nesting technique for optimal feature approximation.
result Optimal features found from data samples using off-the-shelf architectures and optimizers.
Deep neural networks perform well on local tasks but struggle with global tasks.
problem Understanding the limitations of overparameterized deep neural networks in learning global functions.
method Introduced k-local and k-global functions to study the interplay between depth and function locality. result Depth is beneficial for learning local functions but detrimental to learning global functions.
Proposes a new loss function for causal machine-learning.
problem Lack of a well-defined loss function for causal machine-learning.
method Introduces a novel loss function equal to MSE in a standard regression problem.
result Demonstrates that gradient descent can be directly applied to this loss function.
Develops a new method to learn kernels directly over function space.
problem Learning kernels for flexible function approximators.
method Functional Kernel Learning (FKL) using transformed Gaussian processes over spectral densities.
result Direct inference of functional posteriors over kernels enables rich representations.
Study on distributional TD learning with linear approximations for better return estimation.
problem Estimating the return distribution of a policy in reinforcement learning.
method Finite-sample analysis of distributional TD learning with linear function approximation, using the linear-categorical Bellman equation and exponential stability arguments for products of random matrices.
result Sample complexity of linear distributional TD learning matches that of classic linear TD learning, indicating similar difficulty in estimating return distribution versus its expectation.
Proposes a new neural network architecture combining MLP and basis functions.
problem Function approximation and operator learning in scientific machine learning.
method Combines robust MLP inner functions with flexible basis functions outer functions.
result KKAN outperforms MLPs and KANs in function approximation and operator learning tasks.