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.
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.
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 method solves complex bilevel optimization problems.
problem Challenging bilevel optimization problems in machine learning.
method Penalty-based bilevel gradient descent (PBGD) algorithm.
result PBGD algorithm converges for constrained bilevel problems.
Develops an algorithm for bilevel optimization with coupled constraints.
problem Challenges in bilevel optimization with coupled constraints.
method Primal-dual-assisted penalty approach and a fully first-order algorithm (BLOCC).
result Established rigorous convergence theory and demonstrated effectiveness on real-world applications.
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. 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. 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.
Improved penalty-based methods for bilevel optimization with reduced complexity.
problem Suboptimal complexity in solving bilevel optimization problems with large penalty terms.
method Novel penalty reformulation that decouples upper and lower-level variables, enabling larger step sizes and reduced iteration complexity.
result PBGD-Free algorithm that avoids inner loops for coupled constraint BLO problems, with reduced iteration complexity.
This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists in minimizing a convex empirical risk function subject to an ℓ 1 \ell^1 ℓ 1 constraint, a pairwise ℓ ∞ \ell^\infty ℓ ∞ constraint, or a pairwise ℓ 1 \ell^1 ℓ 1 constraint. …
Improved few-shot learning with lower-level neural network embeddings.
problem Limited data scenarios in few-shot learning.
method Graph-based meta-learning framework using hidden layer feature embeddings.
result Utilization of lower-level neural network embeddings improves classifier accuracy.
A new algorithm solves bilevel optimization with linear constraints.
problem Solving bilevel optimization problems with coupled linear constraints.
method Penalty and augmented Lagrangian methods reformulate the problem; a single-loop, first-order algorithm proposed.
result Improved convergence rates compared to prior methods.
Kernel SIVI improves variational inference by avoiding lower-level optimization.
problem Intractable densities in semi-implicit variational distributions.
method Kernel SIVI-SM uses a minimax formulation and kernel tricks to avoid lower-level optimization.
result Kernel Stein discrepancy (KSD) objective is computable and leads to convergence guarantees.
Novel methods for accelerating optimization in complex bilevel and minimax problems.
problem Optimization challenges in bilevel and minimax problems, especially when strong convexity assumptions are not met.
method Accelerated fully first-order methods for Bilevel Optimization (BLO) and Minimax Optimization (NCSC).
result State-of-the-art complexity for finding approximate second-order stationary points in BLO and NCSC.
New method circumvents non-convexity in bilevel RL via hyper-gradient.
problem Non-convexity in lower-level RL problems in bilevel reinforcement learning.
method Characterizing hyper-gradient via fully first-order information, circumventing convexity assumption.
result Developed model-based and model-free algorithms with convergence rate O ( ε − 1 ) O(ε^{-1}) O ( ε − 1 ) . Hierarchical reinforcement learning (HRL) is a promising approach to extend traditional reinforcement learning (RL) methods to solve more complex tasks. Yet, the majority of current HRL methods require careful task-specific design and on-policy training, making them difficult to apply in real-world scenarios. In this p…
Kernel semi-implicit variational inference improves variational inference without additional optimization.
problem Intractability of hierarchical semi-implicit distributions in variational inference.
method Kernel semi-implicit variational inference (KSIVI) using kernel methods to eliminate lower-level optimization.
result KSIVI reduces variational inference to kernel Stein discrepancy (KSD) optimization, improving expressiveness and tractability.
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.
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.
Learning and memory are intertwined in our brain and their relationship is at the core of several recent neural network models. In particular, the Attention-Gated MEmory Tagging model (AuGMEnT) is a reinforcement learning network with an emphasis on biological plausibility of memory dynamics and learning. We find that …
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.
Semiparametric method removes bias in functional bilevel gradient estimation.
problem First-order bias in plug-in hypergradient when lower-level problem is nonparametric.
method Semiparametric debiasing theory based on efficient influence function leads to cross-fitted orthogonal hypergradient estimator.
result Asymptotic normality and uniform control over outer parameter established for the estimator.
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.
Study on stochastic hypergradient computation for machine learning problems.
problem Efficient computation of hypergradients in machine learning models.
method Stochastic approximation schemes for hypergradient computation, focusing on empirical risk minimization.
result Bounds for the mean square error of hypergradient approximation under contraction assumptions.
A new method optimizes diffusion models for fine-tuning tasks efficiently.
problem Optimizing diffusion models for downstream tasks using nested bilevel structures.
method Formalizes the challenge as a generative bilevel optimization problem and introduces a first-order bilevel framework.
result Our method outperforms existing fine-tuning and hyperparameter search baselines.
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. Studying the M-branes leads us naturally to new structures that we call Membrane-, Membrane^c-, String^K(Z,3)- and Fivebrane^K(Z,4)-structures, which we show can also have twisted counterparts. We study some of their basic properties, highlight analogies with structures associated with lower levels of the Whitehead tow…
The paper compares unrolling and bilevel optimization for learning variational models.
problem Learning variational models in supervised learning.
method Analyzes unrolling and bilevel optimization approaches for variational models.
result Unrolling can be better than bilevel optimization, but performance depends on parameters.
This work improves generative models by using feedback from multiple dependent models.
problem Improving the performance of generative models in multi-agent systems.
method Building a hierarchical set-up of multiple dependent generative models and using feedback to improve lower-level models.
result The technique improves the performance of lower-level generative models under certain conditions.
Improved prediction of hierarchical time series using structured regularization.
problem Making coherent forecasts for hierarchical time series.
method Structured regularization method for bottom-level time series predictions.
result Superior prediction accuracy and computational efficiency compared to previous methods.
Unified framework for decentralized bilevel optimization with various heterogeneity-correction strategies.
problem Decentralized bilevel optimization with neighborhood communications and data heterogeneity.
method SPARKLE: Single-loop Primal-dual Algorithm for decentralized bilevel optimization, incorporating various heterogeneity-correction techniques.
result Unified convergence analysis for SPARKLE with state-of-the-art convergence rates compared to existing algorithms.
AdaRL improves robust RL by adaptively adjusting policy complexity.
problem Handling epistemic uncertainty in environment dynamics.
method Bi-level optimization framework with adaptive rank adjustment.
result AdaRL outperforms existing methods on MuJoCo benchmarks.
Paper resolves ambiguity in non-convex bilevel optimization problems.
problem Ambiguity in bilevel optimization with non-convex lower-level objectives.
method Introduces selection maps to define critical points and resolves ambiguity.
result Validates new analytical tools in Morse theory for implicit differentiation.
The hierarchical structure of production planning has the advantage of assigning different decision variables to their respective time horizons and therefore ensures their manageability. However, the restrictive structure of this top-down approach implying that upper level decisions are the constraints for lower level …
We introduce a simple recurrent variational auto-encoder architecture that significantly improves image modeling. The system represents the state-of-the-art in latent variable models for both the ImageNet and Omniglot datasets. We show that it naturally separates global conceptual information from lower level details, …
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. Paper tackles multi-block min-max optimization with applications in deep AUC maximization.
problem Multi-block min-max bilevel optimization with non-convex strongly-concave upper level and strongly convex lower level.
method Single-loop randomized stochastic algorithm for constant number of blocks per iteration.
result Sample complexity of O(1/ε^4) for finding ε-stationary point, matching optimal complexity.
Paper improves stochastic bilevel optimization methods for highly-smooth problems.
problem Finding ε ε ε -stationary points in stochastic bilevel optimization. method Proposes F 2 {}^2 2 SA- p p p methods using p p p th-order finite differences for hyper-gradient approximation. result Achieves upper complexity bound of i l d e O ( p ε − 4 − p / 2 ) ilde{\mathcal{O}}(p ε^{-4-p/2}) i l d e O ( p ε − 4 − p /2 ) for p p p th-order smooth problems. 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).
Variational Auto-Encoders have often been used for unsupervised pretraining, feature extraction and out-of-distribution and anomaly detection in the medical field. However, VAEs often lack the ability to produce sharp images and learn high-level features. We propose to alleviate these issues by adding a new branch to c…
Identifying the flavour of neutral B B B mesons production is one of the most important components needed in the study of time-dependent C P CP C P violation. The harsh environment of the Large Hadron Collider makes it particularly hard to succeed in this task. We present an inclusive flavour-tagging algorithm as an upgrade of…
Learning long-term dependencies is a key long-standing challenge of recurrent neural networks (RNNs). Hierarchical recurrent neural networks (HRNNs) have been considered a promising approach as long-term dependencies are resolved through shortcuts up and down the hierarchy. Yet, the memory requirements of Truncated Bac…
Paper tackles RL for power grid topology optimization.
problem Managing large action spaces in growing power networks.
method Hierarchical multi-agent reinforcement learning (MARL) framework.
result MARL framework outperforms single-agent RL methods.
In this research, we develop a trading strategy for the discrete-time optimal liquidation problem of large order trading with different market microstructures in an illiquid market. In this framework, the flow of orders can be viewed as a point process with stochastic intensity. We model the price impact as a linear fu…
New algorithm solves complex optimization problems efficiently.
problem Minimizing convex upper-level functions over optimal lower-level solutions.
method Reformulates bilevel problems into functionally constrained problems, achieving near-optimal rates.
result Achieves near-optimal rates for both smooth and nonsmooth problems.
Neural NMF discovers hierarchical topics in multilayer data.
problem Detecting latent hierarchical structure in multilayer data.
method Recursive application of nonnegative matrix factorization (NMF) in layers with backpropagation optimization.
result Neural NMF outperforms other hierarchical NMF methods in synthetic and real-world datasets.
Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is computationally challenging. One heuristic to circumvent this difficulty is to use t…
We present the Video Ladder Network (VLN) for efficiently generating future video frames. VLN is a neural encoder-decoder model augmented at all layers by both recurrent and feedforward lateral connections. At each layer, these connections form a lateral recurrent residual block, where the feedforward connection repres…