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Found 61 papers, 7 papers with code
The Role of Inherent Bellman Error in Offline Reinforcement Learning with Linear Function Approximation
Our main structural assumption is that the MDP has low inherent Bellman error, which stipulates that linear value functions have linear Bellman backups with respect to the greedy policy.
Linear Bellman Completeness Suffices for Efficient Online Reinforcement Learning with Few Actions
One of the most natural approaches to reinforcement learning (RL) with function approximation is value iteration, which inductively generates approximations to the optimal value function by solving a sequence of regression problems.
Edit Distance Robust Watermarks for Language Models
We aim for watermarks which satisfy: (a) undetectability, a cryptographic notion introduced by Christ, Gunn & Zamir (2024) which stipulates that it is computationally hard to distinguish watermarked language model outputs from the model's actual output distribution; and (b) robustness to channels which introduce a constant fraction of adversarial insertions, substitutions, and deletions to the watermarked text.
Structure learning of Hamiltonians from real-time evolution
We study the problem of Hamiltonian structure learning from real-time evolution: given the ability to apply $e^{-\mathrm{i} Ht}$ for an unknown local Hamiltonian $H = \sum_{a = 1}^m \lambda_a E_a$ on $n$ qubits, the goal is to recover $H$.
Exploration is Harder than Prediction: Cryptographically Separating Reinforcement Learning from Supervised Learning
We also show that there is no computationally efficient algorithm for reward-directed RL in block MDPs, even when given access to an oracle for this regression problem.
Precise Error Rates for Computationally Efficient Testing
Our result shows that the spectrum is a sufficient statistic for computationally bounded tests (but not for all tests).
Learning quantum Hamiltonians at any temperature in polynomial time
Anshu, Arunachalam, Kuwahara, and Soleimanifar (arXiv:2004. 07266) gave an algorithm to learn a Hamiltonian on $n$ qubits to precision $\epsilon$ with only polynomially many copies of the Gibbs state, but which takes exponential time.
Exploring and Learning in Sparse Linear MDPs without Computationally Intractable Oracles
The key assumption underlying linear Markov Decision Processes (MDPs) is that the learner has access to a known feature map $\phi(x, a)$ that maps state-action pairs to $d$-dimensional vectors, and that the rewards and transitions are linear functions in this representation.
Tensor Decompositions Meet Control Theory: Learning General Mixtures of Linear Dynamical Systems
In this work we give a new approach to learning mixtures of linear dynamical systems that is based on tensor decompositions.
A New Approach to Learning Linear Dynamical Systems
Linear dynamical systems are the foundational statistical model upon which control theory is built.
Minimax Rates for Robust Community Detection
In this work, we study the problem of community detection in the stochastic block model with adversarial node corruptions.
Distilling Model Failures as Directions in Latent Space
Moreover, by combining our framework with off-the-shelf diffusion models, we can generate images that are especially challenging for the analyzed model, and thus can be used to perform synthetic data augmentation that helps remedy the model's failure modes.
Learning in Observable POMDPs, without Computationally Intractable Oracles
Much of reinforcement learning theory is built on top of oracles that are computationally hard to implement.
Provably Auditing Ordinary Least Squares in Low Dimensions
Measuring the stability of conclusions derived from Ordinary Least Squares linear regression is critically important, but most metrics either only measure local stability (i. e. against infinitesimal changes in the data), or are only interpretable under statistical assumptions.
Planning in Observable POMDPs in Quasipolynomial Time
Our main result is a quasipolynomial-time algorithm for planning in (one-step) observable POMDPs.
Robust Voting Rules from Algorithmic Robust Statistics
Maximum likelihood estimation furnishes powerful insights into voting theory, and the design of voting rules.
A No-go Theorem for Robust Acceleration in the Hyperbolic Plane
In recent years there has been significant effort to adapt the key tools and ideas in convex optimization to the Riemannian setting.
Kalman Filtering with Adversarial Corruptions
In a pioneering work, Schick and Mitter gave provable guarantees when the measurement noise is a known infinitesimal perturbation of a Gaussian and raised the important question of whether one can get similar guarantees for large and unknown perturbations.
Can Q-Learning be Improved with Advice?
In this paper we address the question of whether worst-case lower bounds for regret in online learning of Markov decision processes (MDPs) can be circumvented when information about the MDP, in the form of predictions about its optimal $Q$-value function, is given to the algorithm.
Dictionary Learning Under Generative Coefficient Priors with Applications to Compression
There is a rich literature on recovering data from limited measurements under the assumption of sparsity in some basis, whether known (compressed sensing) or unknown (dictionary learning).
Spoofing Generalization: When Can't You Trust Proprietary Models?
In this work, we study the computational complexity of determining whether a machine learning model that perfectly fits the training data will generalizes to unseen data.
Robust Model Selection and Nearly-Proper Learning for GMMs
Given $\textsf{poly}(k/\epsilon)$ samples from a distribution that is $\epsilon$-close in TV distance to a GMM with $k$ components, we can construct a GMM with $\widetilde{O}(k)$ components that approximates the distribution to within $\widetilde{O}(\epsilon)$ in $\textsf{poly}(k/\epsilon)$ time.
Algorithms from Invariants: Smoothed Analysis of Orbit Recovery over $SO(3)$
Our main result is a quasi-polynomial time algorithm for orbit recovery over $SO(3)$ in this model.
Learning GMMs with Nearly Optimal Robustness Guarantees
In this work we solve the problem of robustly learning a high-dimensional Gaussian mixture model with $k$ components from $\epsilon$-corrupted samples up to accuracy $\widetilde{O}(\epsilon)$ in total variation distance for any constant $k$ and with mild assumptions on the mixture.
Learning to Sample from Censored Markov Random Fields
These are Markov Random Fields where some of the nodes are censored (not observed).
No-go Theorem for Acceleration in the Hyperbolic Plane
In recent years there has been significant effort to adapt the key tools and ideas in convex optimization to the Riemannian setting.
Classification Under Misspecification: Halfspaces, Generalized Linear Models, and Evolvability
In this paper, we revisit the problem of distribution-independently learning halfspaces under Massart noise with rate $\eta$.
Settling the Robust Learnability of Mixtures of Gaussians
This work represents a natural coalescence of two important lines of work: learning mixtures of Gaussians and algorithmic robust statistics.
Online and Distribution-Free Robustness: Regression and Contextual Bandits with Huber Contamination
Our approach is based on a novel alternating minimization scheme that interleaves ordinary least-squares with a simple convex program that finds the optimal reweighting of the distribution under a spectral constraint.
Classification Under Misspecification: Halfspaces, Generalized Linear Models, and Connections to Evolvability
In particular, we study the problem of learning halfspaces under Massart noise with rate $\eta$.
Tensor Completion Made Practical
We show strong provable guarantees, including showing that our algorithm converges linearly to the true tensors even when the factors are highly correlated and can be implemented in nearly linear time.
Fast Convergence for Langevin with Matrix Manifold Structure
In this paper, we study one aspect of nonconvexity relevant for modern machine learning applications: existence of invariances (symmetries) in the function f, as a result of which the distribution p will have manifolds of points with equal probability.
Learning Structured Distributions From Untrusted Batches: Faster and Simpler
We revisit the problem of learning from untrusted batches introduced by Qiao and Valiant [QV17].
Fast Convergence for Langevin Diffusion with Manifold Structure
In this paper, we focus on an aspect of nonconvexity relevant for modern machine learning applications: existence of invariances (symmetries) in the function f, as a result of which the distribution p will have manifolds of points with equal probability.
Polynomial time guarantees for the Burer-Monteiro method
The basic idea is to solve a nonconvex program in $Y$, where $Y$ is an $n \times p$ matrix such that $X = Y Y^T$.
Efficiently Learning Structured Distributions from Untrusted Batches
When $k = 1$ this is the standard robust univariate density estimation setting and it is well-understood that $\Omega (\epsilon)$ error is unavoidable.
Learning Some Popular Gaussian Graphical Models without Condition Number Bounds
While there are a variety of algorithms (e. g. Graphical Lasso, CLIME) that provably recover the graph structure with a logarithmic number of samples, they assume various conditions that require the precision matrix to be in some sense well-conditioned.
Spectral Methods from Tensor Networks
Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although they are not presented this way, can be viewed as spectral methods on matrices built from simple tensor networks.
Efficiently Learning Mixtures of Mallows Models
Mixtures of Mallows models are a popular generative model for ranking data coming from a heterogeneous population.
Optimality and Sub-optimality of PCA I: Spiked Random Matrix Models
Our results leverage Le Cam's notion of contiguity, and include: i) For the Gaussian Wigner ensemble, we show that PCA achieves the optimal detection threshold for certain natural priors for the spike.
Learning Restricted Boltzmann Machines via Influence Maximization
This hardness result is based on a sharp and surprising characterization of the representational power of bounded degree RBMs: the distribution on their observed variables can simulate any bounded order MRF.
Beyond the Low-Degree Algorithm: Mixtures of Subcubes and Their Applications
In contrast, as we will show, mixtures of $k$ subcubes are uniquely determined by their degree $2 \log k$ moments and hence provide a useful abstraction for simultaneously achieving the polynomial dependence on $1/\epsilon$ of the classic Occam algorithms for decision trees and the flexibility of the low-degree algorithm in being able to accommodate stochastic transitions.
Learning Determinantal Point Processes with Moments and Cycles
Determinantal Point Processes (DPPs) are a family of probabilistic models that have a repulsive behavior, and lend themselves naturally to many tasks in machine learning where returning a diverse set of objects is important.
Information Theoretic Properties of Markov Random Fields, and their Algorithmic Applications
As an application, we obtain algorithms for learning Markov random fields on bounded degree graphs on $n$ nodes with $r$-order interactions in $n^r$ time and $\log n$ sample complexity.
Robustly Learning a Gaussian: Getting Optimal Error, Efficiently
We give robust estimators that achieve estimation error $O(\varepsilon)$ in the total variation distance, which is optimal up to a universal constant that is independent of the dimension.
Being Robust (in High Dimensions) Can Be Practical
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors.
Approximate Counting, the Lovasz Local Lemma and Inference in Graphical Models
In this paper we introduce a new approach for approximately counting in bounded degree systems with higher-order constraints.
Message-passing algorithms for synchronization problems over compact groups
Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or SO(3).
Optimality and Sub-optimality of PCA for Spiked Random Matrices and Synchronization
Our results include: I) For the Gaussian Wigner ensemble, we show that PCA achieves the optimal detection threshold for a variety of benign priors for the spike.
Provable Algorithms for Inference in Topic Models
But designing provable algorithms for inference has proven to be more challenging.
Robust Estimators in High Dimensions without the Computational Intractability
We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples.
How Robust are Reconstruction Thresholds for Community Detection?
The stochastic block model is one of the oldest and most ubiquitous models for studying clustering and community detection.
Simple, Efficient, and Neural Algorithms for Sparse Coding
Its standard formulation is as a non-convex optimization problem which is solved in practice by heuristics based on alternating minimization.
Noisy Tensor Completion via the Sum-of-Squares Hierarchy
This is also the first algorithm for tensor completion that works in the overcomplete case when $r > n$, and in fact it works all the way up to $r = n^{3/2-\epsilon}$.
Smoothed Analysis of Tensor Decompositions
We introduce a smoothed analysis model for studying these questions and develop an efficient algorithm for tensor decomposition in the highly overcomplete case (rank polynomial in the dimension).
New Algorithms for Learning Incoherent and Overcomplete Dictionaries
In sparse recovery we are given a matrix $A$ (the dictionary) and a vector of the form $A X$ where $X$ is sparse, and the goal is to recover $X$.
A Polynomial Time Algorithm for Lossy Population Recovery
This improves on algorithm of Wigderson and Yehudayoff that runs in quasi-polynomial time for any $\mu > 0$ and the polynomial time algorithm of Dvir et al which was shown to work for $\mu \gtrapprox 0. 30$ by Batman et al.
A Practical Algorithm for Topic Modeling with Provable Guarantees
Topic models provide a useful method for dimensionality reduction and exploratory data analysis in large text corpora.
Provable ICA with Unknown Gaussian Noise, with Implications for Gaussian Mixtures and Autoencoders
We present a new algorithm for Independent Component Analysis (ICA) which has provable performance guarantees.
Algorithms and Hardness for Robust Subspace Recovery
We give an algorithm that finds $T$ when it contains more than a $\frac{d}{n}$ fraction of the points.
Learning Topic Models - Going beyond SVD
Topic Modeling is an approach used for automatic comprehension and classification of data in a variety of settings, and perhaps the canonical application is in uncovering thematic structure in a corpus of documents.
