Framework learns linear programs from optimal decisions.
problem Learning linear programs from optimal decisions is challenging.
method Gradient-based framework for learning linear programs from optimal decisions.
result Successfully learns linear programs and multi-commodity flow instances.
Optimizes pure exploration in linear bandits with a new algorithm.
problem Best-arm identification in linear stochastic bandits.
method Developed the first asymptotically optimal algorithm for fixed-confidence pure exploration in linear bandits.
result Avoids the pitfall of a simple but difficult instance and bypasses the need to solve an optimal design problem.
Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient combinatorial algorithms, but whose non-linear convex counterpart is harder and …
Characterizes problems solvable via linear convergence algorithms.
problem Optimization problems solvable with linear convergence.
method Riemannian gradient descent.
result Characterized problems solvable via linear convergence.
New approach reduces unconstrained linear bandits to simpler optimization problems.
problem Unconstrained linear bandits problem.
method Perturbation-based approach combined with comparator-adaptive OLO algorithms.
result First high-probability guarantees for both static and dynamic regret in unconstrained linear bandits.
BLAE solves batched linear bandits with optimal regret and practical performance.
problem Batched linear bandit problem with limited adaptivity.
method Integrates arm elimination with regularized G-optimal design, achieving minimax optimal regret.
result Achieves minimax optimal regret in both large- K K K and small- K K K regimes with O ( log log T ) O(\log\log T) O ( log log T ) batches. Optimizes PnL using linear signals in quantitative finance.
problem Maximizing profit and loss in financial trading.
method Unsupervised machine learning approach that maximizes Sharpe Ratio through linear relationships and parameter optimization.
result Empirical validation and effectiveness of the model on U.S. Treasury ETF.
Optimal algorithm for identifying best arm in stochastic linear bandits with fixed confidence.
problem Identifying the best arm in stochastic linear bandits with fixed confidence.
method Extending an algorithm designed for Best Arm Identification to the ε ε ε -Thresholding Bandit Problem (TBP). result Asymptotically optimal algorithm for TBP.
Graph neural networks improve solving linear optimization problems.
problem Improving the efficiency of solving linear optimization problems.
method Using graph neural networks to simulate standard interior-point methods for linear optimization problems.
result Graph neural networks can solve linear optimization problems close to optimality, often outperforming conventional solvers.
pyLOT library simplifies machine learning on 3D point clouds via linearized optimal transport.
problem Performing machine learning tasks on 3D point clouds.
method Linearized optimal transport (LOT) to embed distributions into Hilbert space, enabling linear machine learning.
result Downstream tasks on embedded representations are simplified to linear operations.
Paper investigates optimal interpolation methods in linear regression.
problem Understanding when interpolating methods generalize well in linear regression.
method Investigates optimal response-linear interpolators using functions linear in the response variable.
result Provides a closed-form expression for the optimal interpolator and shows it can be derived as the limit of gradient descent.
Refined theorem on linear perturbations with applications in singularity theory and optimization.
problem Linear perturbations and their implications in singularity theory and optimization.
method New perspective of Hausdorff measures for refined transversality theorem.
result Applications in singularity theory and optimization.
Unified approach for optimizing predictions in linear programming and inverse problems.
problem Optimizing predictions in linear programming and inverse problems.
method Maximum optimality margin approach.
result Unified approach that balances computational efficiency and theoretical properties.
Algorithm optimizes quantized isotonic regression with log-linear time updates.
problem Optimizing quantized isotonic regression estimations.
method Modified PAVA algorithm for sequential optimization.
result Log-linear time updates for optimal quantized mapping.
Optimal algorithms for non-linear ridge bandits reduce burn-in cost.
problem Non-linear models introduce a burn-in period with fixed cost.
method Two-stage algorithm: find initial action, then treat locally linear.
result Two-stage algorithm is statistically optimal.
LQF linearizes deep models for better interpretability.
problem Lack of interpretability in deep neural networks.
method Simple modifications to architecture, loss function, and optimization.
result Comparable performance to non-linear fine-tuning, with interpretability.
A new method for optimization in diffeological spaces using linearizations.
problem Optimization in spaces with low regularity.
method Generalizing linearization to diffeological spaces and constructing smooth paths.
result Achieving weak convergence to minima or critical values in diffeological spaces.
Optimal linear contracts are possible even with memory in Gaussian settings.
problem Can optimal dynamic contracts be linear when agents control memory processes?
method Developed a methodology for non-Markovian and non-semimartingale settings, showed linear contracts are optimal for one-dimensional models.
result Linear contracts are optimal for one-dimensional models with memory, and for radial effort cost functions in higher dimensions.
The paper studies optimal transport in linear quadratic systems and derives interpolation inequalities.
problem Optimal transport problem in Linear Quadratic optimal control systems.
method Well-posedness of the Monge problem, regularity of optimal transport map, displacement interpolation of measures.
result Derivation of general interpolation inequalities for entropy functionals.
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…
New insights into optimization and generalization for linear models.
problem Understanding the implicit regularization of optimization methods for linear models.
method Investigating the norms minimized by interpolating solutions and using projections to move between solutions.
result Proving that for over-parameterized linear classification, projections onto the data-span enable the use of under-parameterized techniques.
Study optimal execution in financial markets with constraints.
problem Optimal execution with non-negative constraints in a linear price impact model.
method Purely probabilistic approach via non-linear ODE.
result Complete characterization of value and optimal control.
Policy gradient converges to globally optimal policy in nearly linear-quadratic systems.
problem Finding optimal policies in nonlinear control systems with partial information.
method Policy gradient algorithm designed for nearly linear-quadratic regulators with small Lipschitz nonlinear components.
result Policy gradient algorithm converges to globally optimal policy with linear rate.
Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.
problem Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination.
method Near-optimal algorithms with optimal error guarantees, achieving sample complexity n = i l d e O ( d / ε 2 ) n = ilde{O}(d/ε^2) n = i l d e O ( d / ε 2 ) and almost linear runtime. result First sample near-optimal and almost linear-time algorithms with optimal error guarantees for both problems.
Review of privacy-preserving linear models for high-dimensional data.
problem Overfitting and data memorization in high-dimensional linear models.
method Comprehensive comparison of optimization techniques for differentially private high-dimensional linear models.
result Coordinate-optimized algorithms perform best in empirical tests.
The paper studies robust risk measures with linear penalties under uncertain distributions.
problem Risk measurement under distributional uncertainty.
method Robust distortion risk measures with linear penalty function under distributional constraints.
result Explicit characterization of optimal quantile distribution and value function.
ENIAC method optimizes and explores complex RL problems with non-linear policies.
problem Theoretical understanding of non-linear policies in RL with strategic exploration.
method ENIAC, an actor-critic method for non-linear function approximation.
result ENIAC finds near-optimal policies in polynomial exploration rounds under bounded eluder dimension.
Optimizes non-linear outcomes from summed contributions.
problem Maximizing a non-linear function of summed small contributions.
method Derives a scalable descent algorithm leveraging concentration properties.
result Directly optimizes for stated objective, e.g., A/B test success criterion.
New RL algorithm achieves nearly optimal performance for linear MDPs.
problem Optimal reinforcement learning for episodic linear MDPs.
method Weighted linear regression with variance estimator and rare-switching policy.
result Achieves nearly minimax optimal regret i l d e O ( d H 3 K ) ilde O(d\sqrt{H^3K}) i l d e O ( d H 3 K ) . Study non-linear combinatorial bandits with polynomial rewards, finding significant differences from linear cases.
problem Adversarial combinatorial bandits with general non-linear reward functions.
method Extending existing work on adversarial linear combinatorial bandits, analyzing minimax optimal regret for polynomial and non-polynomial reward functions.
result Minimax optimal regret bounds for adversarial combinatorial bandits with general non-linear reward functions.
Non-linear shrinkage isn't optimal for portfolio optimization, especially when asset dependence is non-stationary.
problem Optimizing portfolios with non-stationary asset dependence structures.
method Derived and compared non-linear shrinkage with an optimal target for covariance matrix estimation.
result Non-linear shrinkage can be significantly improved for portfolio optimization.
Study on adaptivity constraints in linear contextual bandits with optimal design.
problem Impact of adaptivity constraints on linear contextual bandits.
method Two models of limited adaptivity: batch learning and rare policy switches. Proposed distributional optimal design.
result Achieves minimax-optimal regret with optimal number of policy switches and batches.
We analyzed optimism in linear and kernel regression models.
problem Understanding predictive complexity in regression models.
method Derived closed-form asymptotic optimism for linear and kernel regression models.
result Scaled optimism is a useful measure for model complexity.
E 4 ^4 4 algorithm optimizes batched linear bandits with minimal regret and batches.
problem Optimizing batched linear bandits for minimal regret.
method Explore-Estimate-Eliminate-Exploit framework with optimal exploration rate.
result Achieves minimax and asymptotic optimality in regret and batch complexity.
Presents SPEED, an algorithm for optimal policy evaluation in linear bandits with heteroscedastic noise.
problem Optimal data collection for policy evaluation in linear bandits with heteroscedastic reward noise.
method Formulated an optimal design for weighted least squares estimates, derived the optimal sample allocation, introduced SPEED algorithm, and derived regret bounds.
result SPEED leads to policy evaluation with MSE comparable to oracle strategy and significantly lower than random policy execution.
The study tests inferences about neural network optimization from linear interpolation of loss landscapes.
problem Understanding the difficulty of neural network optimization problems.
method Linear interpolation of neural network loss landscapes, systematic evaluation of various factors.
result Linear interpolation does not correlate with model performance, challenging prior intuition.
Linear Transformer Block combines MLP and linear attention for near-optimal ICL in linear regression.
problem Achieving near-optimal in-context learning (ICL) risk for linear regression with a Gaussian prior.
method Combines linear attention and MLP components in a Linear Transformer Block (LTB). Establishes correspondence with one-step gradient descent estimators ( G D e x t − β \mathsf{GD} ext{-}\mathbfβ GD e x t − β ). result LTB achieves nearly Bayes optimal ICL risk for linear regression with a Gaussian prior.
Simple linear models outperform complex BO methods in high dimensions.
problem Overcoming the curse of dimensionality in Bayesian optimization.
method Bayesian linear regression with linear kernels, applied to high-dimensional search spaces.
result Simple linear models match or outperform state-of-the-art BO methods in high-dimensional tasks.
ProxSkip achieves linear speedup in distributed non-convex optimization.
problem Achieving linear speedup in distributed non-convex optimization.
method Unified convergence analysis for stochastic non-convex, convex, and strongly convex problems.
result ProxSkip achieves linear speedup in the number of nodes under stochastic gradients.
Efficient algorithms speed up adversarial training for linear models.
problem Adversarial training for linear models is computationally expensive.
method Tailored optimization algorithms for regression and classification.
result Significantly faster convergence rates for large-scale problems.
We provide the first algorithm for online bandit linear optimization whose regret after T rounds is of order sqrt{Td ln N} on any finite class X of N actions in d dimensions, and of order d*sqrt{T} (up to log factors) when X is infinite. These bounds are not improvable in general. The basic idea utilizes tools from con…
New algorithm for offline RL with linear approx in MDPs and MGs, nearly optimal.
problem Offline RL with linear function approximation in MDPs and MGs.
method Pessimism-based algorithm with uncertainty decomposition via reference function.
result Nearly minimax optimal performance in offline RL for MDPs and MGs.
Optimal unimodal fitting for linear loss functions in a sequential, efficient manner.
problem Optimal unimodal transformation of univariate model scores under linear loss functions.
method Proposes a sequential approach to estimate the optimal rectangular fit for observed samples with each new sample.
result Sequential approach achieves optimal efficiency with logarithmic time complexity per iteration.
Optimal execution strategy for merger & acquisition contracts with price impact.
problem Optimal execution and pricing of financial derivatives in M&A deals.
method Indifference utility arguments, considering linear and nonlinear contracts.
result Linear contracts are more expensive and vulnerable to manipulation.
Optimal control in changing systems without strong convexity assumptions.
problem Adversarial changes in convex costs for unknown linear systems.
method Non-convex lower confidence bounds and computationally-efficient regret minimization.
result Achieves T \smash{\sqrt{T}} T -regret rate, optimal compared to best stabilizing controller. In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse problems as applied to system identification, we show that near-optimal distributed con…
The paper explores optimal algorithms for linear regression under covariate shift, proving the optimality of certain transformations and SGD variants.
problem Optimal algorithms for linear regression under covariate shift with ellipse-shaped constraints.
method Establishes a tight lower generalization bound via Bayesian Cramer-Rao inequality, proves the optimality of certain transformations, and analyzes SGD variants.
result Optimal estimators and SGD variants achieve optimality under specific conditions.
Randomized exploration in linear bandits achieves optimal regret bounds.
problem Optimizing exploration in high-dimensional linear bandit problems.
method Analysis of Thompson sampling without forced optimism.
result Randomized exploration algorithms achieve an O ( d n log ( n ) ) O(d\sqrt{n} \log(n)) O ( d n log ( n )) regret bound in smooth, strongly convex action spaces.