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.
Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear space), equivalently, on random closed sets. …
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…
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 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 ) 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.
Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called Continuous Online Learning (COL), where the gradient of online loss function cha…
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. 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…
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. 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.
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.
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…
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.
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.
We prove a Liouville property for any f f f -harmonic function with polynomial growth on a complete noncompact smooth metric measure space ( M , g , e − f d v ) (M,g,e^{-f}dv) ( M , g , e − f d v ) when the Bakry-Émery Ricci curvature is nonnegative and its diameter of geodesic sphere has sublinear growth.
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 . 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.
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…
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.
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.
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.
New sublinear sketches improve ANN and KDE for massive data streams.
problem Efficiently approximate nearest neighbors and kernel density estimation in large datasets.
method Developed sublinear space and query time algorithms for ANN and A-KDE in streaming and sliding-window models.
result Achieved near-optimal trade-offs between memory size and approximation error for ANN.
New algorithm tackles delayed feedback in Lipschitz bandits with sublinear regret.
problem Delayed feedback in Lipschitz bandits.
method Design of algorithms for bounded and unbounded stochastic delays.
result Sublinear regret guarantees for both bounded and unbounded delays.
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. Algorithm maximizes revenue-risk by estimating price impact kernel and optimizing control problems.
problem Maximizing revenue-risk in a risky asset liquidation with unknown price impact.
method Alternates exploration and exploitation phases, uses novel kernel estimation and stability results.
result Sublinear regret achieved with high probability.
New algorithms save computation in agnostic learning with membership queries.
problem Efficiently learning touchstone classes with membership queries.
method Designing agnostic learning algorithms for circuits with sublinear gates.
result Agnostic learning algorithms for circuits with sublinear gates achieve significant computational savings.
The alternating gradient descent (AGD) is a simple but popular algorithm which has been applied to problems in optimization, machine learning, data ming, and signal processing, etc. The algorithm updates two blocks of variables in an alternating manner, in which a gradient step is taken on one block, while keeping the …
Memory-limited learning tackles adversarial bandits with reduced storage.
problem Adversarial bandit problem with limited memory storage.
method Hierarchical learning policy with sublinear memory requirement.
result Established sublinear regret bounds for weak and shifting regrets.
New algorithms reduce communication for sparse mean estimation in noisy distributed systems.
problem Sparse normal means estimation with limited communication in a distributed setting.
method Two distributed algorithms for estimating a sparse mean vector with sublinear communication.
result Correct support of the sparse mean can be recovered with significantly less communication than previously required.
Paper tackles constrained bandit problems with a new learning framework.
problem Optimizing a black-box reward function subject to a black-box constraint function over a continuous space.
method Rectified Pessimistic-Optimistic Learning (RPOL) framework, incorporating optimistic and pessimistic GP bandit learning.
result RPOL achieves sublinear regret and minimal cumulative constraint violation.
Study on optimal rates for sequential probability assignment using smoothed analysis.
problem Optimal rates for sequential probability assignment under smoothed adversaries.
method General-purpose reduction from minimax rates to transductive learning, development of an efficient algorithm using MLE oracle.
result Optimal (logarithmic) fast rates for parametric and finite VC dimension classes, sublinear regret for general classes.
This work addresses dynamic KDE data structures with robustness to adversarial queries.
problem Efficient KDE data structures for dynamic changing data distributions.
method Developed a theoretical framework for KDE data structures that support subquadratic space, sublinear updates, and adaptive queries.
result Theoretical framework and practical implementation of KDE data structures robust to adversarial queries.
New method connects CAT(0) spaces to hyperbolic spaces.
problem Injecting sublinear Morse boundaries into Gromov boundaries.
method Developed curtain machinery to characterize sublinear Morse properties.
result Continuous injection of sublinear Morse boundaries into Gromov boundaries.
Study tackles nonlinear factor models with unknown monotone links from incomplete and noisy data.
problem Learning nonlinear factor models with unknown monotone links from incomplete and noisy data.
method Formulated as joint recovery of low-rank factors, loadings, and nonlinear link function; proposed BCD algorithm with regularization.
result Established convergence guarantees and sublinear regret bounds for link-function updates.