TensorPlan algorithm finds δ-optimal policies with poly(H,d) queries under linearly realizable state-value function.
problem Efficient planning in MDPs with linearly realizable state-value function.
method TensorPlan algorithm using poly((dH/δ)A) simulator queries. result First algorithm with polynomial query complexity using only linear-realizability of a single competing value function.
Neural network training is usually accomplished by solving a non-convex optimization problem using stochastic gradient descent. Although one optimizes over the networks parameters, the main loss function generally only depends on the realization of the neural network, i.e. the function it computes. Studying the optimiz…
New bandit algorithm works without realizability assumption.
problem Contextual bandit problems without realizability assumption.
method Computes a constrained regression problem in every epoch, ensuring similar regret guarantees as realizability-based algorithms.
result Ensures similar regret guarantees as realizability-based algorithms, up to a misspecification term.
Neural networks cannot approximate certain functions in Sobolev spaces, leading to unbounded parameter growth.
problem Non-closedness of sets of neural networks in Sobolev spaces.
method Construction of sequences of neural networks whose realizations converge to functions not realizable by neural networks.
result Sets of realized neural networks are not closed in order-(m−1) Sobolev spaces Wm−1,p for p∈[1,∞]. New algorithms estimate Q-functions under partial coverage and realizability, improving offline RL guarantees.
problem Offline RL with limited exploration and assumptions about data coverage and Q-function realizability.
method Proposes minimax learning algorithms to estimate soft or vanilla Q-functions with L2-convergence guarantees. result PAC guarantees for offline RL under partial coverage and realizability conditions.
Study of loss functions for learning to defer, proving consistency.
problem Learning to defer in machine learning.
method Introduced a family of surrogate losses parameterized by Ψ and proved their consistency. result Proved realizable H-consistency and Bayes-consistency of specific surrogate losses. A new model forecasts financial risks using multiple realized measures.
problem Forecasting financial risks using multiple realized measures.
method Developed a semi-parametric joint VaR and ES forecasting framework using realized measures.
result The proposed model outperformed other models in forecasting financial risks.
The paper solves graph realization problems for Reeb graphs of Morse functions.
problem Realizing graphs as Reeb graphs with specific preimage configurations.
method Constructing Morse functions with prescribed preimages.
result Solved realization problems for certain types of graphs.
In the case of smooth manifolds, we use Forman's discrete Morse theory to realize combinatorially any Thom-Smale complex coming from a smooth Morse function by a couple triangulation-discrete Morse function. As an application, we prove that any Euler structure on a smooth oriented closed 3-manifold has a particular rea…
This study connects ReLU neural networks to toric geometry to analyze function realization.
problem Determining which continuous piecewise linear functions can be realized by ReLU neural networks.
method Established a connection between toric geometry and ReLU neural networks, defining key structures like the ReLU fan, toric variety, and Cartier divisor.
result Proved a criterion for functions realizable by unbiased shallow ReLU networks using intersection numbers.
New offline RL method works with limited data and function approximators.
problem Sample efficiency with limited data and weak function approximators.
method Pessimistic algorithm based on version space formed by marginalized importance sampling (MIS), with gap assumption.
result Guarantees sample efficiency for simple algorithm under specific assumptions.
New combinatorial framework for geometric realizations of subword complexes.
problem Proving or disproving geometric realizations of subword complexes of Coxeter groups.
method Algebraic combinatorics and discrete geometry framework, parameter matrices.
result Existence of parameter matrices equivalent to realizability of subword complexes as chirotopes.
Analytic realization of Thom-Smale complex for G-manifolds.
problem Realizing Thom-Smale complex for G-manifolds with Lie group action.
method Using G-invariant Witten instanton complex associated with a Morse-Bott function.
result Generalized Thom-Smale complex for G-manifolds including horizontal direction influence.
We analyze realized volatilities constructed using high-frequency stock data on the Tokyo Stock Exchange. In order to avoid non-trading hours issue in volatility calculations we define two realized volatilities calculated separately in the two trading sessions of the Tokyo Stock Exchange, i.e. morning and afternoon ses…
This work provides guarantees for off-policy function estimation under realizability assumptions.
problem Estimating the value function of a policy under user-specified error-measuring distributions.
method The approach involves imposing a flexible regularization on the MIS objectives to account for an arbitrary user-specified distribution.
result Exact characterization of the optimal dual solution that determines the data-coverage assumption in the case of value-function learning.
Lower bounds on Bayes risk for realizable models derived using information theory.
problem Deriving lower bounds on Bayes risk for realizable machine learning models.
method Information-theoretic analysis using rate-distortion theory and mutual information.
result Lower bounds on Bayes risk for realizable models, matching known bounds up to logarithmic factors.
A new model framework called Realized Conditional Autoregressive Expectile (Realized-CARE) is proposed, through incorporating a measurement equation into the conventional CARE model, in a manner analogous to the Realized-GARCH model. Competing realized measures (e.g. Realized Variance and Realized Range) are employed a…
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.
A very simple R3 realization of the Möbius strip, significantly simpler than the common one, is given. For any, however large width/length ratio of the strip, it is shown that this realization, in contrast with the common one, is the union of a vertical segment and the graph of a simple rational function on …
Breaks the hardness conjecture for batch RL with a novel tournament-based approach.
problem Sample-efficient reinforcement learning from exploratory data.
method BVFT algorithm using pairwise comparison and state-action partition.
result Solves the learning problem in a setting previously thought impossible.
Study shows how to realize Ricci curvature as Reeb vector field for contact 3-manifolds.
problem When can a function be realized as Ricci curvature of a Reeb vector field?
method Topological tools to show realization, resolving singularities depend on contact topology.
result Every admissible function can be realized as Ricci curvature for a singular metric away from a measure zero set.
In this work, we propose a new Gaussian process regression (GPR) method: physics information aided Kriging (PhIK). In the standard data-driven Kriging, the unknown function of interest is usually treated as a Gaussian process with assumed stationary covariance with hyperparameters estimated from data. In PhIK, we compu…
The study compares econometric and deep learning models for forecasting COMEX copper futures volatility.
problem Forecasting volatility of COMEX copper futures across different time intervals.
method Econometric models (GARCH, HAR) and deep learning models (RNN, LSTM, GRU) applied to daily and hourly data.
result Deep learning models outperform econometric models in hourly data, but HAR remains the best overall for daily data.
The Hessian Topology is a subject having interesting relations with several areas, for instance, differential geometry, implicit differential equations, analysis and singularity theory. In this article we study the problem of realization of a real plane curve as the Hessian curve of a smooth function. The plane curves …
New method realizes planar graphs as Reeb graphs of algebraic functions.
problem Realizing planar graphs as Reeb graphs of algebraic functions.
method Generic embedding and elementary procedures.
result Generically embedded planar graphs are homeomorphic to Reeb graphs of algebraic functions.
New method constructs smooth functions with specific Reeb graphs and preimages on 3D manifolds.
problem Construct smooth functions with prescribed Reeb graphs and preimages on 3D closed manifolds.
method Develops a new approach to realize graphs as Reeb graphs of smooth functions on 3D closed manifolds.
result Provides a best possible solution for functions on 3D closed manifolds.
We characterize the fractional Dehn twist coefficient of a braid in terms of a slope of the homogenization of the Upsilon function, where Upsilon is the function-valued concordance homomorphism defined by Ozsváth, Stipsicz, and Szabó. We use this characterization to prove that n-braids with fractional Dehn twist coef…
Synthetic proof shows globally hyperbolic Lorentzian spaces with specific curvature are warped products.
problem Synthetic proof of rigidity for globally hyperbolic Lorentzian spaces.
method Synthetic geometry and warped product analysis.
result Spaces with specific curvature and distance realizer are warped products.
New algorithms for interactive learning match minimax bounds efficiently.
problem Interactive learning in the realizable setting with computational efficiency.
method General framework, computationally efficient algorithms, Monte Carlo hit-and-run sampling.
result Sample complexities quantifiable in terms of combinatorial quantities, computationally efficient.
New method efficiently evaluates policies using trajectory data.
problem Statistically efficient policy evaluation with limited data.
method Trajectory-based approach for policy evaluation.
result Improved sample complexity for policy evaluation.
New RL method learns to skip states in linearly qπ-realizable MDPs, simplifying to linear MDPs.
problem Online RL in episodic MDPs with linearly qπ-realizable action-values. method Derives a novel algorithm that learns to skip states and applies a linear MDP algorithm.
result First polynomial-sample-complexity online RL algorithm for linearly qπ-realizable MDPs. Asymptotic analysis of short-maturity options on realized variance in local-stochastic volatility models.
problem Analyzing the behavior of short-maturity options on realized variance in local-stochastic volatility models.
method Large deviations theory and variational problems to solve rate functions for different cases.
result Explicit solutions for the rate function in the uncorrelated case and upper/lower bounds and expansions for the correlated case.
This paper tackles deferral learning with multiple experts, providing strong theoretical guarantees.
problem Optimizing input assignment to experts balancing accuracy and computational cost.
method Introducing new surrogate loss functions and efficient algorithms with strong theoretical learning guarantees.
result Realizable H-consistency, H-consistency bounds, and Bayes-consistency for deferral learning. We consider the following problem: given two parallel and identically oriented bundles of light rays in n-dimensional Euclidean space and given a diffeomorphism between the rays of the former bundle and the rays of the latter one, is it possible to realize this diffeomorphism by means of several mirror reflections? We …
Directly applies Kazdan--Warner results to prescribe scalar curvature on bundles.
problem Prescribing scalar curvature functions on bundles.
method Direct application of Kazdan--Warner results and variational methods.
result Determines which functions are realizable as scalar curvature functions on bundles.
Study shows realizable learnability doesn't imply agnostic learnability for distributions.
problem Learnability and robustness of distribution classes.
method Analyzes the relationship between learnability and robustness for distribution learning.
result Realizable learnability does not imply agnostic learnability for distributions.
Optimal algorithm for maximizing rewards in contextual bandits with resource constraints.
problem Maximizing rewards in contextual bandits with resource constraints.
method Proposed a universal and optimal algorithmic framework for CBwK by reducing it to online regression.
result Established the optimality of the proposed algorithm for various function classes.
We prove that, up to homeomorphism, any graph subject to natural necessary conditions on orientation and the cycle rank can be realized as the Reeb graph of a Morse function on a given closed manifold M. Along the way, we show that the Reeb number R(M), i.e. the maximum cycle rank among all Reeb graphs of…
We obtained that any 2-form and any smooth function on 2-manifolds with boundary can be realized as the curvature form and the gaussian curvature function of some Riemmanian metric, respectively.
Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal function approximation in an arbitrarily high dimensional Euclidian space. It is show…
Radial-basis-function networks are traditionally defined for sets of vector-based observations. In this short paper, we reformulate such networks so that they can be applied to adjacency-matrix representations of weighted, directed graphs that represent the relationships between object pairs. We re-state the sum-of-squ…
Paper tackles offline RL with weak assumptions on both function classes and data coverage.
problem Achieve sample-efficient offline RL with weak assumptions on both factors.
method Simple algorithm based on primal-dual formulation of MDPs, with density-ratio function modeling dual variables.
result Polynomial sample complexity achieved under realizability and single-policy concentrability.
We perform return interval analysis of 1-min {\em{realized volatility}} defined by the sum of absolute high-frequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive realized vola…
The problem of immersing a simply connected surface with a prescribed shape operator is discussed. From classical and more recent work, it is known that, aside from some special degenerate cases, such as when the shape operator can be realized by a surface with one family of principal curves being geodesic, the space o…
Compact learning results across various loss functions.
problem Understanding sample complexity in transductive learning.
method Analyzing finite projections and sample complexities for different loss functions.
result Exact compactness of sample complexity holds broadly across realizable and agnostic learning.
BOSH optimizes functions with stochastic evaluations more efficiently and precisely.
problem Optimizing functions with noisy evaluations can lead to suboptimal solutions.
method BOSH uses a hierarchical Gaussian process to generate a growing pool of realizations.
result BOSH provides more efficient and higher-precision optimization than standard BO.
We investigate the problem of the realization of a given graph as the Reeb graph R(f) of a smooth function f:M→R with finitely many critical points, where M is a closed manifold. We show that for any n≥2 and any graph Γ admitting the so called good orientation there exis…
Unified framework for realizable and agnostic learning.
problem Lack of a unified theory for realizable and agnostic learnability.
method Three-line blackbox reduction.
result Unified understanding across various learning settings.