Post-Doctoral Research Visit F/M Stochastic non-smooth optimization by first-order methods

Inria, the French national research institute for the digital sciences; France; Remote; EUR 30,000 - 36,000; Full time

Benefits offered by this job

Public transport reimbursement

Annual leave: 7 weeks + RTT 10 days

Teleworking and flexible working hours

Equipment provided and training access

Social security coverage

Job summary

Inria, the French national research institute for the digital sciences, seeks a postdoctoral researcher to analyse adaptive optimisation algorithms that adjust hyperparameters like the step size based on accumulated data. The project spans the GHOST team and the DAO team of the LJK lab, with funding through the MIAI chair.

The candidate will study AdaGrad variants in nonsmooth settings, contribute to theory, and collaborate with Zuse Institute Berlin and Toulouse's Institut Mathématique.

Qualifications

• Foundation knowledge in numerical optimisation, in particular first-order methods.
• Scientific programming skills (Julia, Python) for empirical validations of algorithms.

Responsibilities

• Identify convergence conditions for adaptive algorithms in various settings.
• Investigate robustness to noises, initialization and initial step-size.
• Compare properties with classical methods such as stochastic gradient descent.
• Disseminate findings via articles, seminars and conferences.

Skills

Numerical optimisation

Programming: Julia

Programming: Python

Tools

Julia

Python

Job description

Inria, the French national research institute for the digital sciences

Organisation/Company Inria, the French national research institute for the digital sciences Research Field Mathematics Researcher Profile Recognised Researcher (R2) Application Deadline 14 Nov 2026 - 00:00 (UTC) Country France Type of Contract Temporary Job Status Full-time Hours Per Week 38.5 Offer Starting Date 1 Jan 2027 Is the job funded through the EU Research Framework Programme? Not funded by a EU programme Reference Number 2026-10616 Is the Job related to staff position within a Research Infrastructure? No

Offer Description

The postdoc will be conducted between the Inria GHOST team and the DAO team of the LJK lab. It will be funded by the Structured Optimization and Learning chair of the MIAI cluster.

The main objective is to analyse and deepen our understanding of adaptive optimisation algorithms which adapt their hyperparameter (e.g., the step size) based on the data accumulated during the optimisation process (e.g., during training in a learning context). This family includes central algorithms such asAdaGrad, RMSProp, Adam, and related variants, which have a key role in the recent development of numerical optimisation. The majority of existing work considers these algorithms applied on smooth functions, and we want to extend this understanding to stochastic, non-convex, and non-smooth optimisation. Those results will contribute to narrow the gap between current theory and the practical applications in which these algorithms are already used, which are non-convex, non-smooth.

To understand the topic: Some important algorithms studied in the smooth case are currently ill-understood when applied to nonsmooth instances. One of the research questions will focus on the definition of a problem class close to learning models and on which nonsmooth algorithms can be analysed.

The postdoctoral researcher is expected to conduct research on AdaGrad algorithms in the nonsmooth setting.

Collaboration: Some collaborations with the Zuse Institute Berlin and the Institut Mathématique de Toulouse will be possible during the working period.

Principal activities

• Identify necessary/sufficient conditions so that adaptive algorithms can converge.
• Investigate the robustness of the optimisation methods, i.e., study qualitative and quantitative properties under the effects of noises, initialization, initial step-size.
• Comparing these properties of adaptive algorithms with those of classical ones, such as (stochastic) gradient descent.
• Identify a zoology of structured optimisation problems, where adaptive algorithms can significantly outperform other families of methods.

Complementary activities

• Disseminating findings via articles, seminars and conferences.

Foundation knowledge in numerical optimisation, in particular on first-order methods.

Scientific programming skills (Julia, Python) for empirical validations of algorithms.

Specific Requirements

Scientific curiosity, analytical skills to understand convergence analysis and lower bounds for numerical optimisation algorithms.

Languages FRENCH Level Basic

Languages ENGLISH Level Good

Additional Information

• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking and flexible organisation of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage under conditions

2927 € gross salary / month