Notes from the 2026 summer school Bilevel Optimization: Theory, Algorithms and AI Applications. The course runs on two threads: a theory track deriving optimality conditions for bilevel programs and MPEC / MPCC through variational analysis (normal cones, coderivatives, value functions, partial calmness), and an algorithms + applications track on gradient-based methods (hypergradients, implicit differentiation) and their use in hyperparameter optimization, meta-learning, and pruning.
Notes
| # | Note | Status |
|---|---|---|
| 1 | Optimality Conditions for MPECs via Variational Analysis | draft |
| 2 | Bilevel Programs: Introduction, Reformulation and Partial Calmness | draft |
Concept Map
- Theory — variational analysis: KKT / Fritz John, constraint qualifications (NNAMCQ / PLICQ, MFCQ); MPCC and its game-theoretic origins (Nash, Stackelberg, Cournot); regular / limiting / Clarke normal cones, Clarke generalized gradient; S- / M- / C-stationarity; MPEC, coderivatives, calmness
- Theory — bilevel programs: value-function approach, sensitivity analysis, partial calmness
- Algorithms: gradient-based bilevel optimization — hypergradients, implicit differentiation, single- / double-loop methods
- Applications: hyperparameter optimization, meta-learning (MAML), model pruning, safe RL
References
- Summer school: Bilevel Optimization: Theory, Algorithms and AI Applications (2026)
- Related roadmap: Stochastic Programming and Bilevel Optimization Roadmap
Planned Notes
- Gradient-based algorithms for bilevel optimization (hypergradients, implicit / iterative differentiation)
- Applications in machine learning (hyperparameter optimization, meta-learning, pruning)