This paper explores optimising acquisition functions in Bayesian optimisation.
problem Optimising acquisition functions in Bayesian optimisation is challenging due to their non-convex nature.
method The authors derive compositional forms for acquisition functions and use them to recast maximisation as a compositional optimisation problem.
result The compositional approach to maximising acquisition functions shows empirical advantages across various tasks.
Paper develops robust SGLD for solving non-convex DRO problems.
problem Solving non-convex distributionally robust optimisation problems with adversarially corrupted samples.
method Developed a Stochastic Gradient Langevin Dynamics (SGLD) algorithm with non-asymptotic convergence bounds.
result The robust SGLD estimator outperforms vanilla SGLD in terms of test accuracy.
New research challenges the independence assumption in neurosymbolic learning, leading to overconfident predictions and unrepresentable uncertainty.
problem The independence assumption in neurosymbolic learning systems can lead to overconfident predictions and hinder uncertainty quantification.
method The study proves the limitations of the independence assumption and introduces new loss functions that are non-convex and difficult to optimise.
result Neurosymbolic learning systems using the independence assumption are prone to overconfidence and cannot represent uncertainty over multiple valid options.
Novel algorithms for entropic optimal transport from an optimisation perspective.
problem Solving the entropic-regularised optimal transport problem.
method Developed novel methods inspired by mirror descent, solving semi-dual problems or non-convex constrained problems over joint distributions.
result Non-asymptotic rates of convergence for the proposed methods under minimal assumptions.
A new optimisation method efficiently scales Hessian-vector products for neural networks.
problem Challenges in applying second-order quasi-Newton methods due to large Hessian and non-convexity.
method Proposes an optimisation algorithm that asymptotically uses the exact inverse Hessian with modified eigenvalues.
result Demonstrates scalability and comparable performance to other optimisation methods in neural networks.
SOBER optimizes and quadrates efficiently in parallel for diverse tasks.
problem Scalability of batch Bayesian optimization and quadrature for expensive functions.
method Reformulates batch selection as a quadrature problem, balancing exploitation and exploration.
result SOBER outperforms 11 baselines on 12 tasks.
A new optimisation framework for neural networks without hyperparameters.
problem Lack of explicit architectural information in optimisation frameworks.
method Extends mirror descent to account for neural architecture, transforming a Bregman divergence.
result Automatic gradient descent: a first-order optimiser without hyperparameters.
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form solutions of proximal operators and envelope representations based on the Moreau, Fo…
New method optimizes multiple points in Bayesian optimization efficiently.
problem Optimizing multiple points in expensive black-box functions.
method Reformulated BO as probability measure optimization, using convex gradient flows.
result Demonstrated effectiveness on various benchmarks compared to state-of-the-art methods.
We consider the problem of inverse kinematics (IK), where one wants to find the parameters of a given kinematic skeleton that best explain a set of observed 3D joint locations. The kinematic skeleton has a tree structure, where each node is a joint that has an associated geometric transformation that is propagated to a…
New algorithm finds sparse matrices on Stiefel manifold for optimisation.
problem Finding sparse matrices on Stiefel manifold for optimisation.
method Modified Orthogonal Iteration algorithm for sparse global optimality.
result Proposed method finds globally optimal sparse Stiefel matrices.
An important task in machine learning and statistics is the approximation of a probability measure by an empirical measure supported on a discrete point set. Stein Points are a class of algorithms for this task, which proceed by sequentially minimising a Stein discrepancy between the empirical measure and the target an…
Analyzes optimal learning rate schedules in high-dimensional non-convex optimization problems.
problem Optimizing high-dimensional non-convex loss landscapes.
method Langevin optimization with learning rate decaying as \(η(t) = t^{-β}\).
result To speed up optimization without getting stuck in saddles, a decay rate \(β < 1\) is optimal, contrary to convex setups where \(β = 1\).
In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they lift the original n×n-dimensional variable to an n2×n2-d…
Unified distributed SGD improves non-convex optimization for large datasets.
problem Bottleneck in scaling SGD for non-convex functions and large datasets.
method Distributed and parallel implementation of SGD (DPSGD) combining asynchronous distribution and lock-free parallelism.
result DPSGD achieves better convergence rate and speed-up with more cores and workers.
Unified theory linking Bayesian and ensemble methods in deep learning.
problem Uncertainty quantification in deep learning.
method Reformulating optimisation as convex optimisation in probability measures, studying Wasserstein gradient flows.
result Unified theory explaining success of deep ensembles over variational inference.
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank constrained optimisation problem. This problem is non-convex and state-of-the-art algor…
The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the computational complexity of solving a non-convex optimisation problem. We propose fin…
This paper tackles batch Bayesian optimal experimental design by using Wasserstein gradient flows.
problem The challenge of optimising high-dimensional, strongly non-convex expected information gain in batch settings.
method Probabilistic lifting to the space of probability measures, entropic regularisation, Wasserstein gradient flow, and particle-based algorithms.
result The proposed approach can be used directly as a randomised batch-design policy or as a computational relaxation.
Scaling Bayesian optimisation (BO) to high-dimensional search spaces is a active and open research problems particularly when no assumptions are made on function structure. The main reason is that at each iteration, BO requires to find global maximisation of acquisition function, which itself is a non-convex optimizati…
New framework converts multi-objective to single-objective optimisation.
problem Solving multi-objective optimisation problems.
method Formalises scalarisation into mathematical framework, uses R2 utilities.
result R2 utilities are monotone and submodular, optimised by greedy algorithms.
Unified Bayesian Optimisation for mixed variables improves performance.
problem Efficient optimisation of problems with both categorical and continuous variables.
method Derive value proposals from the Expected Improvement criterion to optimise both categorical and continuous variables under a single acquisition metric.
result Unified approach significantly outperforms existing methods across mixed-variable tasks.
A new method learns priors for Bayesian optimisation to improve performance.
problem Bayesian optimisation tasks often assume strong similarity, which is violated in many cases.
method Replace strong similarity assumption with shape similarity, learn priors for hyperparameters.
result PLeBO and prior transfer find good inputs in fewer evaluations.
Study improves Bayesian optimisation with ensemble transfer learning.
problem Improving sample efficiency in Bayesian optimisation of expensive functions.
method Empirical analysis of ensemble-based transfer learning methods and pipeline components.
result Two components (warm start initialisation and positive weight constraint) improve transfer learning Bayesian optimisation performance.
AdamZ optimiser improves neural network training efficiency.
problem Challenges in optimisation like overshooting and stagnation.
method Dynamic learning rate adjustment based on overshoot and stagnation factors.
result Consistently minimises loss function, improving model performance.
Wind farm layout optimisation tackles space constraints with Bayesian multi-objective approach.
problem Optimizing wind farm layout due to limited space and conflicting objectives.
method Set-based multi-objective Bayesian optimisation using Gaussian process.
result Demonstrates potential of set-based Bayesian multi-objective optimisation for wind farm layout.
Book covers tools for zeroth-order convex optimisation.
problem Zeroth-order convex optimisation.
method Cutting plane methods, interior point methods, continuous exponential weights, gradient descent, online Newton step.
result Improved existing bounds and algorithms.
Bayesian optimisation tackles high-dimensional categorical and mixed search spaces.
problem Bayesian optimisation on high-dimensional categorical and mixed search spaces is challenging.
method Combining local optimisation with a tailored kernel design.
result Empirically outperforms current baselines in performance and computational costs.
O3 optimizes samples from generative models without extra training.
problem Optimizing specific criteria within rich data distributions.
method Surrogate latent spaces for efficient black-box optimisation.
result Surrogate-space optimisation finds higher-scoring samples.
Bayesian optimisation framework for graph functions.
problem Optimizing functions on graph structures efficiently.
method Learning suitable kernels and local modelling.
result Demonstrated effectiveness on synthetic and real-world graphs.
Bayesian optimisation tackles expensive black-box functions with constraints.
problem Optimizing constrained black-box functions in machine learning and simulation.
method Proposes a new Knowledge Gradient acquisition function for constrained Bayesian optimisation.
result Demonstrates superior performance over four state-of-the-art constrained Bayesian optimisation algorithms.
MTL2L learns to adapt optimisation rules for unseen data.
problem Learners need to adapt to unseen data domains.
method Introduces MTL2L, a context-aware neural optimiser.
result MTL2L can adapt optimisation rules for unseen data.
Real world experiments are expensive, and thus it is important to reach a target in minimum number of experiments. Experimental processes often involve control variables that changes over time. Such problems can be formulated as a functional optimisation problem. We develop a novel Bayesian optimisation framework for s…
Information-theoretic Bayesian optimisation techniques have demonstrated state-of-the-art performance in tackling important global optimisation problems. However, current information-theoretic approaches require many approximations in implementation, introduce often-prohibitive computational overhead and limit the choi…
Bayesian optimisation algorithm for unknown search spaces with sub-linear regret.
problem Efficient optimisation of expensive black-box functions in unknown search spaces.
method Expands search space over iterations based on a hyperharmonic series, scales to high dimensions.
result Sub-linear regret growth for both algorithms.
New methods improve global optimisation for expensive functions using lookahead strategies.
problem Optimising expensive functions without gradient info in high dimensions.
method Nonmyopic acquisition strategies based on approximate dynamic programming.
result Nonmyopic methods outperform myopic approaches in various applications.
Paper introduces deterministic EM approximations for non-convex likelihood functions.
problem Deterministic approximations for the E-step of EM algorithm are lacking.
method Developed a theoretical framework for deterministic approximations, analyzed Riemann sums and tempered EM.
result Proved convergence guarantees for deterministic approximations and new non-trivial temperature profiles.
Deep Optimisation (DO) combines evolutionary search with Deep Neural Networks (DNNs) in a novel way - not for optimising a learning algorithm, but for finding a solution to an optimisation problem. Deep learning has been successfully applied to classification, regression, decision and generative tasks and in this paper…
One-pass optimisation for high-dimensional hyperparameters.
problem Efficient optimisation of hyperparameters in machine learning models.
method Approximate hypergradient-based optimisation for any continuous hyperparameter, requiring only one training episode.
result Competitive performance on various datasets without hyperparameter restarts.
Ensuring that classifiers are non-discriminatory or fair with respect to a sensitive feature (e.g., race or gender) is a topical problem. Progress in this task requires fixing a definition of fairness, and there have been several proposals in this regard over the past few years. Several of these, however, assume either…
Bayesian optimisation is improved by incorporating expert prior through space warping.
problem Cold start phase in expensive function optimisation.
method Prior distribution warps the search space around high probability regions of function optimum.
result Improves optimisation performance through acquisition agnostic approach.
We present an efficient block-diagonal ap- proximation to the Gauss-Newton matrix for feedforward neural networks. Our result- ing algorithm is competitive against state- of-the-art first order optimisation methods, with sometimes significant improvement in optimisation performance. Unlike first-order methods, for whic…
A novel optimisation framework through quadratic nonlinear projection is introduced for credit portfolio when the portfolio risk is measured by Conditional Value-at-Risk (CVaR). The whole optimisation procedure to search toward the optimal portfolio state is conducted by a series of single-step optimisations under the …
In this paper we develop a statistical theory and an implementation of deep learning models. We show that an elegant variable splitting scheme for the alternating direction method of multipliers optimises a deep learning objective. We allow for non-smooth non-convex regularisation penalties to induce sparsity in parame…
New approach separates VAE and GP for better molecular optimisation.
problem Optimizing complex structured domains like molecular spaces using VAEs.
method Decouples VAE for structure generation and GP for predictive modelling, combining them with a Bayesian update rule.
result Improves identification of high-potential candidates in molecular optimisation.
Optimizes data power control in cell-free networks for better spectral efficiency.
problem Maximizing overall spectral efficiency in cell-free networks with multi-objective optimisation.
method Applied scalable multi-objective Bayesian optimisation to solve convergence-time limitations.
result Improved radio resource management in cell-free networks.
Study analyzes a new algorithm for complex optimization problems.
problem Stochastic bilevel optimisation problems in continuous-time models.
method Continuous-time, two-timescale stochastic approximation algorithm.
result Obtained weak convergence rate using central limit theorem.
Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they find good minima instead of being trapped in spurious ones. Here we present a qu…