BILBO optimizes bilevel problems without repeated lower-level optimizations.
problem Challenges in bilevel optimization, especially in noisy, constrained, and derivative-free settings.
method BILevel Bayesian Optimization (BILBO) that optimizes both levels simultaneously, using confidence-bounds and function query selection.
result Theoretical and empirical evidence of BILBO's effectiveness on various problems.
Novel method for bilevel optimization with convex lower-level problem.
problem Minimizing a smooth objective over the optimal solution set of a convex constrained problem.
method Local cutting plane approximation of lower-level solution set combined with conditional gradient updates.
result Achieves optimal iteration complexity for the considered class of bilevel problems.
Paper explores generalization of AID-based bi-level optimization methods.
problem Uncertainty in generalization properties of AID-based bi-level optimization methods.
method Uniform stability analysis and convergence study of AID-based methods.
result AID-based methods can achieve similar generalization as single-level nonconvex problems.
New algorithm stabilizes bi-level hyperparameter optimization.
problem Stability issues in bi-level hyperparameter optimization.
method Uses Moreau-Yosida regularization to stabilize convergence.
result Significant improvement in loss values with fixed computation budget.
Paper tackles efficient SGD methods for constrained bilevel optimization.
problem Stochastic bilevel optimization with equality constraints.
method Alternating implicit projected SGD and its variants.
result Achieves sample complexity matching state-of-the-art for unconstrained problems.
New framework tackles bi-level optimization without LLS condition.
problem Bi-level optimization problems without LLS condition.
method Bi-level Descent Aggregation (BDA) framework, proving convergence without LLS condition.
result Proves convergence of BDA without LLS condition.
This paper analyzes user-level local differential privacy in distributed systems.
problem The relationship between user-level and item-level local differential privacy under the local model is complex.
method The paper analyzes the mean estimation problem and applies it to stochastic optimization, classification, and regression. It proposes adaptive strategies to achieve optimal performance at all privacy levels.
result The proposed methods are minimax optimal up to logarithmic factors and show that user-level DP can lead to faster convergence rates than item-level DP.
New algorithm optimizes adaptive return level for Markowitz portfolios.
problem Finding an optimal return level for Markowitz portfolios when investor's risk appetite is unknown.
method Krasnoselskii-Mann Proximity Algorithm based on proximity operator and momentum technique.
result Significant improvements over state-of-the-art methods in portfolio optimization.
MAML optimizes shared priors for subtasks in a nonconvex meta-objective.
problem Understanding global optimality of MAML for nonconvex meta-objectives.
method Characterizes optimality gap of MAML stationary points via first-order optimization methods.
result Establishes global optimality of MAML for both RL and supervised learning.
A new algorithm improves Wasserstein discriminant analysis for better data classification.
problem Improving data classification in machine learning.
method Bi-level nonlinear eigenvector algorithm (WDA-nepv) for optimal transport and trace ratio optimizations.
result WDA-nepv enhances classification accuracy and scalability.
New method achieves optimal sample complexity without warm-start in bilevel optimization.
problem Optimizing smooth objective functions with fixed point constraints in meta-learning and equilibrium models.
method Fixed point iterations at lower-level and projected inexact gradient descent at upper-level.
result Achieves near optimal sample complexity O ( ε − 2 ) O(ε^{-2}) O ( ε − 2 ) and i l d e O ( ε − 1 ) ilde{O}(ε^{-1}) i l d e O ( ε − 1 ) samples. The paper finds optimal levels for traders in mean-reverting markets.
problem Determining optimal levels for traders in mean-reverting markets.
method Analytical framework using heat potentials.
result Developed an analytical solution for optimal levels.
Study optimal retirement time and consumption with habitual persistence.
problem Understanding retirement consumption patterns with habitual persistence.
method Established concise habitual evolution, used martingale and duality methods.
result Optimal consumption declines sharply at retirement but excess consumption increases.
New methods solve complex optimization problems without strong convexity assumptions.
problem Complex bilevel optimization problems with minimax lower-level structures.
method Penalty-based first-order methods for bilevel minimax optimization.
result Achieves ε ε ε -KKT point with improved oracle complexity. This paper optimizes predicting support and resistance levels in financial markets.
problem Optimizing prediction of resistance and support levels in financial markets.
method Assuming a constant elasticity of variance process, the paper derives optimal trading boundaries using the aspiration level hypothesis.
result Optimal trading boundaries serve as predictors of resistance and support levels, located relative to the median interval of the hidden aspiration level.
New algorithm tackles nested bi-level optimization problems for robust feature learning.
problem Nested compositional bi-level optimization problems in machine learning.
method Stochastic approximation algorithms for solving nested compositional bi-level optimization problems without matrix inversions.
result Achieves an ε-stationary solution with an oracle complexity of approximately O_T(1/ε^2).
New methods solve complex optimization problems in machine learning.
problem Challenges in stochastic bilevel optimization with constraints and high variables.
method Inexact bilevel stochastic gradient methods for constrained and unconstrained lower-level problems.
result Comprehensive convergence theory for both unconstrained and constrained cases.
This paper considers nonlinear regular-singular stochastic optimal control of large insurance company. The company controls the reinsurance rate and dividend payout process to maximize the expected present value of the dividend pay-outs until the time of bankruptcy. However, if the optimal dividend barrier is too low t…
New methods optimize complex optimization problems with improved efficiency.
problem Optimizing complex problems with a convex lower-level objective.
method Uses stochastic cutting planes and conditional gradient updates.
result Improves complexity for both convex and non-convex upper-level functions.
SUSTAIN algorithm tackles stochastic bilevel optimization with near-optimal complexity.
problem Stochastic bilevel optimization problems with specific convexity and smoothness properties.
method SUSTAIN algorithm using single-timescale double-momentum stochastic approximation.
result SUSTAIN achieves near-optimal complexity for finding ε-stationary solutions.
New method for optimizing complex composite functions with reduced variance.
problem Optimizing multi-level composite functions with nested random and smooth mappings.
method Normalized proximal approximate gradient (NPAG) method with nested stochastic variance reduction.
result Total sample complexity of O ( ε − 3 ) O(ε^{-3}) O ( ε − 3 ) in expectation and O ( N + N ε − 2 ) O(N+\sqrt{N}ε^{-2}) O ( N + N ε − 2 ) in finite-sum cases. A method for fair representation learning through bi-level optimization and implicit differentiation.
problem Ensuring fair predictors invariant across sub-groups.
method Bi-level optimization with inner-loop for invariant predictors, implicit path alignment for efficiency.
result Consistently better trade-off in prediction performance and fairness measurement.
Paper optimizes GEMM for deep learning models, improving performance.
problem Limited GEMM optimization in deep learning frameworks restricts performance on different hardware.
method Proposes two novel algorithms: Greedy Best First Search (G-BFS) and Neighborhood Actor Advantage Critic (N-A2C) based on TVM framework.
result Significant performance improvements in GEMM computation time, achieving up to 40% savings.
New method uses bi-level optimization to learn useful representations for imitation learning.
problem Learning useful representations for multiple tasks in imitation learning settings.
method Formulates representation learning as a bi-level optimization problem.
result Bi-level optimization framework provides sample complexity benefits for imitation learning.
Nonlinear optimal control problems are often solved with numerical methods that require knowledge of system's dynamics which may be difficult to infer, and that carry a large computational cost associated with iterative calculations. We present a novel neurobiologically inspired hierarchical learning framework, Reinfor…
New algorithms protect user-level privacy in learning tasks.
problem Protecting user-level privacy in learning tasks with stringent constraints.
method Proposes algorithms for learning tasks under user-level differential privacy constraints.
result Privacy cost decreases as users provide more samples or as the number of users increases.
In a financial market model, we consider variations of the problem of minimizing the expected time to upcross a certain wealth level. For exponential Levy markets, we show the asymptotic optimality of the growth-optimal portfolio for the above problem and obtain tight bounds for the value function for any wealth level.…
In this paper, we propose a deep multimodal fusion network to fuse multiple modalities (face, iris, and fingerprint) for person identification. The proposed deep multimodal fusion algorithm consists of multiple streams of modality-specific Convolutional Neural Networks (CNNs), which are jointly optimized at multiple fe…
Motivated by the industry practice of pairs trading, we study the optimal timing strategies for trading a mean-reverting price spread. An optimal double stopping problem is formulated to analyze the timing to start and subsequently liquidate the position subject to transaction costs. Modeling the price spread by an Orn…
New algorithms solve complex multi-level optimization problems with improved efficiency.
problem Smooth stochastic multi-level composition optimization problems.
method Two algorithms using moving-average and linearized stochastic estimates.
result Achieved sample complexities of O(1/ε^4) and O(1/ε^6).
The paper optimizes tax implementation delays for insurance companies with Lévy risk processes.
problem Maximizing tax payments and minimizing costs for insurance companies.
method Optimization of tax implementation levels for spectrally negative Lévy insurance risk processes.
result Optimal implementation levels for tax payments and capital injections are derived.
Optimizes query routing to LLMs under cost and resource constraints.
problem Non-uniform or adversarial batching in per-query routing methods leads to cost inefficiency.
method Batch-level, resource-aware routing framework that jointly optimizes model assignment for each batch.
result Robust routing framework improves accuracy by 1-14% over non-robust methods.
Study optimal ridge regularization for out-of-distribution prediction.
problem Optimal ridge regularization for predicting out-of-distribution data.
method Established conditions for optimal regularization under covariate and regression shifts, proving monotonic risk in data aspect ratio.
result Negative regularization can be optimal under shifts, even with isotropic or underparameterized training features.
Generically learns movement control policies from exploration data.
problem Movement optimization in physically based characters.
method Parameterizes actions as target states, learns low-level control policy.
result Improves movement optimization across multiple tasks and algorithms.
New method solves complex optimization problems faster.
problem Minimizing a convex smooth objective over the optimal solution set of another convex smooth problem.
method Uses a cutting plane approach to approximate the lower-level problem and an accelerated gradient method to update the upper-level objective.
result Shows that the method requires at most O ( max { 1 / ε f , 1 / ε g } ) \mathcal{O}(\max\{1/\sqrt{ε_{f}}, 1/ε_g\}) O ( max { 1/ ε f , 1/ ε g }) iterations to achieve ε f ε_f ε f -suboptimality and ε g ε_g ε g -infeasibility. Trajectory-level supervision allows efficient offline reinforcement learning.
problem Offline reinforcement learning
method Developing a statistical theory for offline policy optimization from trajectory-level labels
result Proving a high-probability guarantee of order O ~ ( H 2 C s a ( π ⋆ ) / n ) \widetilde O(H^2\sqrt{C_{sa}(\pi^\star)/n}) O ( H 2 C s a ( π ⋆ ) / n ) A multilevel optimization method for constrained problems.
problem Regularized constrained linear inverse problems with box constraints.
method Geometric multilevel optimization with varying discretization levels.
result Preserves feasibility of updates while speeding up computations.
Optimal gradient quantization reduces communication costs in distributed deep learning.
problem High communication costs in distributed training of deep neural networks.
method Deduced optimal gradient quantization conditions for binary and multi-level quantization, developed novel schemes for dynamic quantization levels.
result Demonstrated superior performance of proposed quantization schemes on CIFAR and ImageNet datasets.
Two-tier approach optimizes RL hyper-parameters for better agent learning.
problem Optimizing hyper-parameters in reinforcement learning to improve agent performance.
method Two-step optimization: first categorical hyper-parameters, then solution-level hyper-parameters.
result Promising results in simulated control tasks, suggesting user-independent reinforcement learning applications.
MiLeNAS improves neural architecture search by reducing approximation errors and achieving better accuracy.
problem Improving efficiency and accuracy in neural architecture search (NAS).
method Mixed-level reformulation (MiLeNAS) to optimize efficiently and reliably.
result MiLeNAS achieves lower validation error and higher accuracy than bilevel optimization methods.
This paper proves IRM minimizes o.o.d. risk under certain conditions.
problem Deep networks can fail to generalize to new domains with different distributions.
method Proves IRM minimizes o.o.d. risk through a bi-level optimization problem.
result IRM minimizes o.o.d. risk under specific conditions.
Paper proposes SMO for solving bilevel optimization problems efficiently.
problem Solving bilevel optimization problems with nonsmooth convex lower-level and nonconvex upper-level objectives.
method Sequential minimax optimization (SMO) method using modified augmented Lagrangian and penalty schemes.
result Improves operation complexity for finding ε \varepsilon ε -KKT solutions. New method tackles inexact bilevel optimization for faster parameter learning.
problem Nested optimization problems in bilevel learning with computationally difficult exact solutions.
method Inexact derivative-free optimization algorithms for approximate lower-level solutions.
result Global convergence and worst-case complexity for the proposed approach.
BiDVL improves EBLVMs for visual tasks by optimizing two variational distributions.
problem Training EBLVMs is challenging due to intractable distributions.
method Bi-level doubly variational learning with two tractable distributions.
result BiDVL achieves impressive image generation and reconstruction performance.
A new stochastic method tackles bi-level optimization problems in deep learning.
problem Bi-level optimization problems in deep learning, including hyperparameter optimization and meta learning.
method Turning a BLO problem into a stochastic optimization, using SGLD MCMC and a recurrent algorithm to compute MC-estimated hypergradient.
result Our method is more robust to suboptimal inner optimization and non-unique inner minima, leading to more reliable solutions.
Proposes methods for online conformal prediction with nested prediction sets across multiple confidence levels.
problem Need for uncertainty quantification with multiple confidence levels in diverse applications.
method Online optimization perspective to enforce nestedness of prediction sets while controlling quantile estimation error.
result Achieves stable coverage across all levels, strictly nested prediction sets, and improved efficiency.
This work optimizes mean estimation under varying privacy constraints.
problem Mean estimation with heterogeneous privacy constraints.
method Proposes an algorithm for mean estimation under different privacy levels for users.
result Shows a saturation phenomenon in performance as privacy levels are relaxed.
Estimates population mean from user-level data with privacy, accounting for heterogeneity.
problem Heterogeneous user data with varying numbers of data points and distributions.
method Simple model of heterogeneous user data, differential privacy mechanism for estimation.
result Asymptotic optimality of the proposed estimator and general lower bounds on error.