arXiv research

This paper analyzes the sample complexity of two timescale reinforcement learning algorithms.

Gradient-based temporal difference (GTD) algorithms are widely used in off-policy learning scenarios. Among them, the two time-scale TD with gradient correction (TDC) algorithm has been shown to have superior performance. In contrast to previous studies that characterized the non-asymptotic convergence rate of TDC only…

This paper improves tail dependence analysis by introducing a path-based approach.

We devise a distributional variant of gradient temporal-difference (TD) learning. Distributional reinforcement learning has been demonstrated to outperform the regular one in the recent study \citep{bellemare2017distributional}. In the policy evaluation setting, we design two new algorithms called distributional GTD2 a…

This study improves convergence of two-timescale SA under Markovian noise in reinforcement learning.

We study two time-scale linear stochastic approximation algorithms, which can be used to model well-known reinforcement learning algorithms such as GTD, GTD2, and TDC. We present finite-time performance bounds for the case where the learning rate is fixed. The key idea in obtaining these bounds is to use a Lyapunov fun…

The paper analyzes the sample complexities for policy evaluation with linear function approximation.

New measures capture tail dependence and non-exchangeability in financial data.

Paper introduces MTCM to measure multivariate tail dependence.

Paper analyzes Greedy-GQ for reinforcement learning with Markovian noise.

RO-TD learns sparse value functions efficiently.

New TD algorithms stabilize RL tasks by reformulating updates into fixed point equations.

Tabular in-context learners perform well on biomolecular tasks, but performance depends on the representation used.

Investigates linearity of group amalgams and new examples of non-linear groups.

Classifies linear embeddings of grassmannians and ind-grassmannians.

New classifier combines locally linear kernels for fast and accurate non-linear classification.

Analyzes neural networks using linear models to understand their behavior.

Paper presents a machine learning method to improve significance tests for misspecified linear models.

Yu. I. Merzljakov developed a method of splittable coordinates which helps to verify the linearity of some groups, he established some fundamental results using this method. In this paper we use the method of splittable coordinates and find some sufficient condition under which the semi--direct product of two linear gr…

In this paper we give an example of a linear group such that its tensor square is not linear. Also, we formulate some sufficient conditions for the linearity of non-abelian tensor products $G \otimes H$ and tensor squares $G \otimes G$. Using these results we prove that tensor squares of some groups with one relation a…

We prove that the semistability growth of hyperbolic groups is linear, which implies that hyperbolic groups which are sci (simply connected at infinity) have linear sci growth. Based on the linearity of the end-depth of finitely presented groups we show that the linear sci is preserved under amalgamated products over f…

Non-linear Hopf manifolds can be embedded into linear ones and admit LCK metrics.

The paper proves that linearization along trajectories preserves flatness in discrete-time systems.

Unified derivation of high-dimensional linear models using stochastic gradient descent.

Linear F-manifolds are studied with connections and dual spaces.

Efficiently extracts linear dynamics from complex observations.

The paper analyzes the generalizability of linear autoencoders and multivariate linear regression.

In this paper we derive a differential identity for linearized gravity on the Kerr spacetime and more generally on vacuum spacetimes of Petrov type D. We show that a linear combination of second derivatives of the linearized Weyl tensor can be formed into a complex symmetric 2-tensor $\mathcal{M}_{ab}$ which solves the…

Improved regret bound for linear ensemble sampling.

Linear Transformer Block combines MLP and linear attention for near-optimal ICL in linear regression.

In this paper, we give complete classifications of linear $\infty$-harmonic maps between Euclidean and Heisenberg spaces, between Nil and Sol spaces. We also classify all $\infty$-harmonic linear endomorphisms of Sol space and show that there is a subgroup of $\infty$-harmonic linear automorphisms in the group of linea…

LoLCATs improves linearized LLM quality with less memory and compute.

SSL framework identifies non-linear systems without labeled data.

Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of regions and region-specific models. This paper proposes novel convex region-specific…

Study finds exact limits for sparse regression with fewer observations than usual.

LQF linearizes deep models for better interpretability.

Develops estimators for near-optimal linear regression under distribution shift.

In a paper with Jean-Paul Dufour in 1999 \cite{DufourZung-Nambu1999}, we gave a classification of linear Nambu structures, and obtained linearization results for Nambu structures with a nondegenerate linear part. There was a case left open in \cite{DufourZung-Nambu1999}, namely the case of smooth linearization of Nambu…

BELIEF framework interprets GLMs using binary linear models.

In many European countries the growth of the real GDP per capita has been linear since 1950. An explanation for this linearity is still missing. We propose that in artificial intelligence we may find models for a linear growth of performance. We also discuss possible consequences of the fact that in systems with linear…

A new decision tree variant improves linear model performance.

The parallel linear transports defined by flat linear connection are axiomatically described. On this basis a number of properties, some of which are new, of these transports and connections are derived.

Study local properties of Chern-scalar curvature through linearization stability.

New algorithm learns linear dynamical systems from measurements.

Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the Gaussian processes which encode the linear model either have probability of nearly…

We consider linear slices of the space of Kleinian once-punctured torus groups; a linear slice is obtained by fixing the value of the trace of one of the generators. The linear slice for trace 2 is called the Maskit slice. We will show that if traces converge `horocyclically' to 2 then associated linear slices converge…

Let F_n denote the free group generated by n letters. The purpose of this article is to show that Hol(F_2), the holomorph of the free group on two generators, is linear. Consequently, any split group extension of F_2 by a linear group H is linear. This result gives a large linear subgroup of Aut(F_3). A second applicat…

Characterizes problems solvable via linear convergence algorithms.