Extends sublinear expectations to random sets, identifying extremal and constructing methods.
problem Extending sublinear expectations to random sets.
method Identifying extremal expectations and presenting general construction methods.
result Identification of extremal sublinear and superlinear expectations.
The paper shows how sublinear biLipschitz equivalences affect Morse boundaries of metric spaces.
problem Understanding how sublinear biLipschitz equivalences affect Morse boundaries of metric spaces.
method Defining sublinear biLipschitz equivalence and Morse boundaries, proving invariance under SBEs, using sublinear rays.
result κ-Morse boundaries of proper geodesic metric spaces are invariant under suitable sublinear biLipschitz equivalences.
The paper develops methods for time-varying constrained online convex optimization.
problem Time-varying loss and constraint functions in online convex optimization.
method Model-based augmented Lagrangian methods (MALM) for time-varying and delayed feedback.
result Sublinear regret and constraint violation for both time-varying and delayed feedback scenarios.
New model for Knightian uncertainty with jumps.
problem Knightian uncertainty and non-linear jumps.
method Probabilistic construction of non-linear affine processes with jumps.
result Tractable model for Knightian uncertainty with sublinear expectations.
Sublinear LSVI via LSH reduces runtime to sublinear in actions.
problem Efficiently estimating value functions in reinforcement learning with sublinear runtime.
method Formulated as approximate maximum inner product search, used LSH to solve with sublinear time complexity.
result Sublinear runtime while maintaining LSVI's regret.
For α ∈ ( 1 , 2 ) α\in (1,2) α ∈ ( 1 , 2 ) , we present a generalized central limit theorem for α α α -stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential equations (PIDEs). A classical generalized central limit theorem is recovered as a special case, p…
Efficient algorithm for bandit convex optimization with sublinear regret.
problem Optimizing in unknown convex functions without projection.
method Projection-free algorithm achieving O ( n T 4 / 5 ) O(nT^{4/5}) O ( n T 4/5 ) sublinear regret. result Achieves O ( n T 4 / 5 ) O(nT^{4/5}) O ( n T 4/5 ) sublinear regret for bounded convex functions. Sharp Liouville theorem for minimal graphs on manifolds with nonnegative Ricci curvature.
problem Characterizing smooth solutions to minimal hypersurface equations on manifolds with nonnegative Ricci curvature.
method Gradient estimate for minimal graphs over Σ Σ Σ with small linear growth of the negative parts of graphic functions via iteration. result Every smooth solution u u u to minimal hypersurface equation on Σ Σ Σ is a constant provided u u u has sublinear growth for its negative part. The paper analyzes the asymptotic sequential Rademacher complexity for finite function classes.
problem Understanding the complexity of finite function classes in asymptotic settings.
method Using viscosity solutions of a G-heat equation and sublinear expectation theory, the paper derives the asymptotic sequential Rademacher complexity.
result The asymptotic sequential Rademacher complexity is expressed in terms of the viscosity solution of a G-heat equation and the expected value of the largest order statistics of a multidimensional G-normal random variable.
The output scores of a neural network classifier are converted to probabilities via normalizing over the scores of all competing categories. Computing this partition function, Z Z Z , is then linear in the number of categories, which is problematic as real-world problem sets continue to grow in categorical types, such as …
New algorithms for constrained online optimization with memory and predictions.
problem Control of constrained dynamical systems and scheduling with reconfiguration budgets.
method Proposed algorithms achieving sublinear regret and constraint violation under time-varying constraints, both with and without predictions.
result First algorithms achieving sublinear regret and constraint violation in constrained online optimization with memory.
New algorithm optimizes functions in Matérn kernel RKHS with noisy feedback.
problem Optimizing functions in RKHS of Matérn kernel with noisy bandit feedback.
method π-GP-UCB algorithm with guaranteed sublinear regret for all ν > 1 and d ≥ 1.
result First practical approach with guaranteed sublinear regret for all ν > 1 and d ≥ 1.
Paper proposes quantum methods for optimizing machine learning functions.
problem Machine learning optimization problem
method Average approach and Partial Swap Test Cut-off method (PSTC)
result Potential to improve PSTC to O ( ∣ Θ ∣ ⋅ s u b l i n e a r N ) O(\sqrt{|Θ|} \cdot sublinear \ N) O ( ∣Θ∣ ⋅ s u b l in e a r N ) The paper tackles online optimization with continuous submodular functions, achieving sublinear regret bounds.
problem Online optimization with continuous submodular functions.
method Proposes Frank-Wolfe algorithm and online stochastic gradient ascent for continuous submodular maximization.
result Achieves O ( T ) O(\sqrt{T}) O ( T ) regret bounds against ( 1 − 1 / e ) (1-1/e) ( 1 − 1/ e ) -approximation and 1 / 2 1/2 1/2 -approximation in hindsight. Paper shows AGD variant converges to better stationary solutions.
problem Optimization problems with nonconvex objectives.
method Perturbed Alternating Gradient Descent (PA-GD) algorithm.
result PA-GD converges to second-order stationary solutions with sublinear rate.
GP-UCB resolves sublinear regret for kernelized bandits.
problem Minimizing regret in kernelized bandit problems.
method Using a new regularization technique for kernel ridge estimators, improving GP-UCB's sublinear regret rate.
result GP-UCB achieves nearly optimal sublinear regret for the Matérn kernel.
Sublinear time kernel approximations using structured matrices.
problem Efficiently approximating kernel functions in sublinear time.
method Structured matrices and random embeddings for Gaussian vectors.
result Structured matrices can approximate kernel functions in sublinear time.
New algorithms learn high-dimensional LMMs with sublinear complexity.
problem Computational infeasibility of learning LMMs on big data.
method Sublinear algorithms using dual estimators and randomized techniques.
result Theoretical and practical robustness of parameter estimation.
The purpose of the paper is to characterize the dimension of sublinear Higson corona ν L ( X ) ν_L(X) ν L ( X ) of X X X in terms of Lipschitz extensions of functions: Theorem: Suppose ( X , d ) (X,d) ( X , d ) is a proper metric space. The dimension of the sublinear Higson corona ν L ( X ) ν_L(X) ν L ( X ) of X X X is the smallest integer m ≥ 0 m\ge 0 m ≥ 0 with the following property…
New algorithm controls systems with unknown, changing losses.
problem Control systems with adversarial perturbations and unknown loss function.
method Efficient sublinear regret algorithm for bandit convex optimization with memory.
result Achieves efficient control with sublinear regret in the presence of unknown, changing losses.
Extends tracking guarantees for time-varying variational inequalities.
problem Tracking solutions of time-varying variational inequalities.
method Extends existing results to sublinear solution paths and periodic problems.
result Discrete dynamical systems of periodic time-varying VI can exhibit chaotic behavior or converge to the solution.
Quantum algorithm speeds up Gibbs partition function estimation.
problem Estimating partition functions in sublinear time.
method Sublinear-time quantum algorithm using quantum phase and amplitude estimation.
result First sublinear-time speed-up for partition function estimation.
Paper tackles stochastic k k k -submodular bandits with full feedback, achieving sublinear regret.
problem Online optimization of k k k -submodular functions with full-bandit feedback. method Proposes online algorithms for various k k k -submodular stochastic combinatorial multi-armed bandit problems. result Achieves sublinear α α α -regret bounds for multiple k k k -submodular stochastic combinatorial multi-armed bandit problems. New RL algorithm achieves sublinear regret and constraint violation without simulators.
problem Maximizing reward under utility constraints in large-scale systems.
method Model-free, simulator-free algorithm using LSVI-UCB with primal-dual optimization and soft-max policy.
result Achieves i l d e O ( d 3 H 3 T ) ilde{\mathcal{O}}(\sqrt{d^3H^3T}) i l d e O ( d 3 H 3 T ) regret and i l d e O ( d 3 H 3 T ) ilde{\mathcal{O}}(\sqrt{d^3H^3T}) i l d e O ( d 3 H 3 T ) constraint violation bounds. The aim of this paper is to introduce the sublinear Higson corona and show that the sublinear Higson corona of Euclidean cone of P and X is decomposed into the product of P and that of X. Here P is a compact metric space and X is unbounded proper metric space. For example, the sublinear Higson corona of n-dimensional E…
Posterior sampling-based EI achieves sublinear regret bounds for expensive function optimization.
problem Theoretical analysis of expected improvement (EI) in Bayesian optimization.
method Randomized posterior sampling of EI.
result Achieves sublinear Bayesian cumulative regret bounds.
New setup for online learning captures continuous changes in losses, improving dynamic regret analysis.
problem Capturing regularity in online learning problems with continuous changes in losses.
method Introducing Continuous Online Learning (COL) and proving its equivalence to solving certain equilibrium problems (EPs).
result Achieving sublinear dynamic regret in COL is equivalent to solving certain EPs, offering conditions for efficient algorithms.
We study the growth of harmonic functions on complete Riemann-ian manifolds where the extrinsic diameter of geodesic spheres is sublinear. It is an generalization of a result of A. Kazue. We also get a Cheng and Yau estimates for the gradient of harmonic functions.
Efficient algorithm controls unknown systems with adversarial perturbations.
problem Controlling unknown linear systems with adversarial perturbations and convex losses.
method Measures regret against an optimal linear policy, provides efficient algorithm with sublinear regret bound.
result First efficient algorithm with sublinear regret bound of T^{2/3}.
Sublinear algorithms detect cliques in graphs with high probability.
problem Detecting a planted clique in random graphs efficiently.
method Non-adaptive low-degree polynomial queries of adjacency matrix entries.
result Sublinear time detection is possible for a specific range of clique sizes.
The paper defines conditional nonlinear expectations for specific function spaces.
problem Defining conditional nonlinear expectations for specific function spaces.
method Develops a sublinear increasing functional and a set-valued mapping to represent conditional expectations.
result Characterizes the existence and properties of conditional nonlinear expectations.
We give a proof of the sublinear tracking property for sample paths of random walks on various groups acting on spaces with hyperbolic-like properties. As an application, we prove sublinear tracking in Teichmueller distance for random walks on mapping class groups, and on Cayley graphs of a large class of finitely gene…
Study projection in acylindrically hyperbolic groups, proving sublinear tracking and growth bounds.
problem Projection phenomena in acylindrically hyperbolic groups.
method Analyzing shortest projections in word metrics and hyperbolic spaces.
result Sublinear tracking of shortest projections and effective growth bounds.
SmoothFBO tackles non-stationary functional bilevel optimization.
problem Current FBO methods are limited to static offline settings and perform poorly in online, non-stationary scenarios.
method SmoothFBO introduces a time-smoothed stochastic hypergradient estimator with a window parameter to handle non-stationarity.
result SmoothFBO achieves sublinear regret and outperforms existing methods in non-stationary hyperparameter optimization and model-based reinforcement learning.
Single-timescale actor-critic finds globally optimal policy.
problem Finding globally optimal policy in reinforcement learning.
method Simultaneous actor and critic updates with linear or deep neural network approximations.
result Actor sequence converges to globally optimal policy at O ( K − 1 / 2 ) O(K^{-1/2}) O ( K − 1/2 ) rate. Paper proposes OPF policy for fair resource allocation with sublinear regret.
problem Fair resource allocation in an online setting against an unrestricted adversary.
method Online Proportional Fair (OPF) policy achieving approximate sublinear regret.
result OPF policy achieves c α c_α c α -approximate sublinear regret with c α ≤ 1.445 c_α \leq 1.445 c α ≤ 1.445 . Estimates learnability from small data, showing accuracy with few samples.
problem Estimating how well a model class can fit a distribution of labeled data.
method Sublinear sample size estimation for learnability, extending to non-isotropic settings.
result Accurate estimation of learnability with O ( d ) O(\sqrt{d}) O ( d ) samples, even for noisy labels. New algorithm reduces prediction error in online learning without knowing base measure.
problem Smoothed online learning without knowledge of base measure.
method R-Cover algorithm based on recursive coverings.
result First algorithm to guarantee sublinear regret for agnostic smoothed online learning without prior knowledge of base measure.
New framework guides resource usage to achieve sublinear regret in adversarial settings.
problem Achieving sublinear regret in online decision making with changing reward and cost distributions.
method General primal-dual methods guided by spending plans that ensure balanced resource usage.
result Achieves sublinear regret with respect to spending plans that balance resource usage.
A new method solves convex optimization problems on manifolds efficiently.
problem Optimization on Hadamard manifolds with convex objectives.
method Intrinsic Riemannian proximal gradient method.
result Sublinear and linear convergence rates for convex and strongly convex problems, respectively.
We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an optional sampling theorem that…
Paper analyzes complexity of proximal inertial gradient descent.
problem Computational complexity of proximal inertial gradient descent.
method Analyzed convergence rates and proved various rates under different conditions.
result Proved non-ergodic O(1/k) rate for coercive objective functions.
A new federated algorithm reduces regret in X-armed bandit problems.
problem Collaborative optimization of heterogeneous local objectives.
method Fed-PNE algorithm using hierarchical partitioning and weak smoothness.
result Achieves sublinear cumulative regret with minimal communication.
New setup for continuous online learning improves understanding of imitation learning.
problem Challenges in capturing regularity in online problems.
method Continuous Online Learning (COL) setup, focusing on continuous gradient changes.
result Fundamental equivalence between sublinear dynamic regret and solving certain EPs.
Stochastic algorithm achieves sublinear convergence for bi-objective optimization.
problem Optimizing two conflicting functions using gradient or subgradient descent.
method Stochastic alternating algorithm with varying steps for each objective.
result Achieves sublinear convergence rate of O(1/T) under strong convexity.
Inexact acquisition solutions in BO lead to sublinear cumulative regret.
problem Inexact maximization of acquisition functions in Bayesian optimization.
method Define inaccuracy measure, establish cumulative regret bounds for GP-UCB and GP-TS.
result Inexact BO algorithms can achieve sublinear cumulative regret under appropriate inaccuracy conditions.
CD methods tackle nonconvex optimization with three terms, achieving critical points.
problem Minimizing nonconvex functions with specific structure.
method Developed randomized CD, randomly permuted CD, and accelerated CD methods.
result CD methods converge to critical points with sublinear complexity.
Algorithm learns multiple tasks with minimal planning, achieving near-optimal performance.
problem Learning multiple tasks efficiently in a reinforcement learning setting.
method UCB Lifelong Value Distillation (UCBlvd) algorithm with structural assumption for shared exploration.
result Sublinear regret bound of i l d e O ( ( d 3 + d ′ d ) H 4 K ) ilde{\mathcal{O}}(\sqrt{(d^3+d^\prime d)H^4K}) i l d e O ( ( d 3 + d ′ d ) H 4 K ) with O ( d H log ( K ) ) \mathcal{O}(dH\log(K)) O ( d H log ( K )) planning calls.