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Lindon Roberts

Lecturer

University of Sydney

Biography

I am a lecturer and ARC DECRA Fellow at the School of Mathematics and Statistics, University of Sydney. My research interests are in numerical analysis and data science, particularly nonconvex and derivative-free optimization.

Details of my CV, publications, talks and software are below (or look at Google Scholar and Github). For general optimization resources, see below or my nonlinear optimization resources page.

Recent news:

News archive

Awards:

Interests

  • Derivative-Free Optimization
  • Nonconvex Optimization
  • Numerical Analysis
  • Data Science

Education

  • DPhil in Mathematics, 2019

    University of Oxford

  • Bachelor of Computational Science (Honours), 2011

    Australian National University

Research

Optimization

Optimization—finding the maximum or minimum of a function—is one of the most important classes of problem in computational mathematics, arising often in scientific and industrial applications. My focus is on nonlinear optimization, where the function to be optimized (the ‘objective’ function) is some nonlinear, possibly nonconvex function usually with little known structure.

Nonlinear optimization resources

Together with Coralia Cartis and Jaroslav Fowkes (University of Oxford), I maintain a page of resources for nonlinear optimization, including a collection of software and test problems.

Derivative-Free Optimization (DFO)

Generally speaking, to optimize a nonlinear objective, you approximate it locally by some simpler function (such as a low-order Taylor series). To construct this simpler function, you need to evaluate the objective and its derivatives at some set of points. Evaluating the derivative of the objective can be done in several ways:

  • If you know the analytic form of the objective, you can compute its derivatives using calculus.
  • If you have access to computer code for evaluating the objective, automatic differentiation could be used to compute analytic derivatives.
  • Otherwise, you have to approximate the derivative, e.g. using finite differencing.

However, if the objective is black-box, expensive to evaluate or noisy (e.g. a Monte Carlo simulation, or involves the finite termination of an iterative procedure), these approaches may be impractical or inaccurate. Derivative-free optimization (DFO) is the field devoted to nonlinear optimization of objectives when you only have access to (possibly inaccurate) evaluations of the objective.

My research

I develop and study model-based DFO algorithms. This is a class of DFO method which tries to incorporate features of derivative-based methods, and ultimately build local approximations to the objective (e.g. by polynomial interpolation). I have developed several algorithms and software packages for solving least-squares problems with DFO methods, and developed techniques which make model-based DFO more robust to noise, able to local minima, and tackle large-scale problems via dimensionality reduction.

Employment

[2022 – present] Lecturer, University of Sydney

[2019 – 2022] MSI Fellow, Australian National University

[2015 – 2019] Doctoral Student, University of Oxford

[2012 – 2015] Senior Analyst, Macquarie Group

  • Worked in the Quantitative Applications Division of the Risk Management Group. Responsible for implementing risk management models (particularly for market risk) and reviewing pricing models.
  • Macquarie Group is Australia’s largest investment bank, headquartered in Sydney.

Talks

Expected decrease for derivative-free algorithms using random subspaces [slides available]
11 Dec 2023 WOMBAT/WICO 2023
Large-scale derivative-free optimization using random subspace methods [slides available]
1 Sep 2023 Simons Collaboration on Hidden Symmetries and Fusion Energy
Analyzing Inexact Hypgergradients for Bilevel Learning
1 Jun 2023 SIAM OP23
Analyzing Inexact Hypergradients for Bilevel Learning [slides available]
9 Dec 2022 AustMS 2022
Black-Box Optimisation Techniques for Complex Systems [slides available]
29 Nov 2022 Biarri Applied Mathematics Conference
See all talks

Recent Publications

Google Scholar | ORCID

M. S. Salehi, S. Mukherjee, L. Roberts, M. J. Ehrhardt (2024). An adaptively inexact first-order method for bilevel optimization with application to hyperparameter learning.

Preprint

L. Roberts (2024). Model Construction for Convex-Constrained Derivative-Free Optimization.

Preprint

A. Berahas, L. Roberts, F. Roosta (2024). Non-Uniform Smoothness for Gradient Descent. Trans. on Machine Learning Research.

Preprint PDF

M. J. Ehrhardt, L. Roberts (2023). Analyzing Inexact Hypergradients for Bilevel Learning. IMA J. Appl. Math..

Preprint Journal

L. Roberts, C. W. Royer (2023). Direct search based on probabilistic descent in reduced spaces. SIAM J. Optim..

Preprint Code Journal

See all publications

Software

Github | Click on each package for more details. Other useful packages not developed by me are listed on the nonlinear optimization resources webpage

directsearch

Flexible optimization package using direct search (derivative-free) methods
PDF Code

DFBGN

Derivative-free block Gauss-Newton method (for large-scale nonlinear least-squares problems)
PDF Code

trustregion

Python routines for solving trust-region subproblems
Code

PyCUTEst

Python interface to CUTEst optimization testing package
PDF Code

DFO-LS

Derivative-free solver for nonlinear least-squares problems
PDF Code

Py-BOBYQA

General-purpose derivative-free optimization solver
PDF Code

DFO-GN

Derivative-Free Gauss-Newton solver
PDF Code

Teaching

University of Sydney

Australian National University

University of Oxford

Qualifications

  • 2018, Professional Development Framework Supporting Learning Award, Staff and Educational Development Association — this is a teaching qualification accredited by the UK professional association for higher education (more details here), assessed by the University of Oxford.

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