Optimization Theory and Algorithms
The mathematical backbone of modern learning and control. Build a working understanding of convex analysis, optimality conditions and the algorithms that solve large-scale problems in practice.
minx f(x) s.t. g(x) ≤ 0, h(x) = 0
What you will learn
- Convex sets, convex functions and duality
- Optimality conditions: Lagrangian and KKT
- Gradient, proximal, accelerated and stochastic methods
- Newton, quasi-Newton and interior-point methods
- Constrained and nonconvex problems in practice
Prerequisites: linear algebra, multivariable calculus
Learning-Based Safe Control
Combine data-driven models with formal guarantees. Learn to design controllers that improve from experience while provably respecting safety constraints.
ḣ(x, u) ≥ −α(h(x)) keeps h(x) ≥ 0
What you will learn
- Stability and Lyapunov analysis
- Control barrier functions and safety filters
- Model predictive control with learned dynamics
- Gaussian processes and uncertainty-aware models
- Safe exploration and constrained reinforcement learning
Prerequisites: optimization, introductory control theory
Fundamentals of Reinforcement Learning
From Markov decision processes to deep policy optimization. Understand why reinforcement learning algorithms work, when they fail, and how to apply them to sequential decision problems.
V*(s) = maxa [ r(s, a) + γ 𝔼 V*(s′) ]
What you will learn
- Markov decision processes and Bellman equations
- Dynamic programming: value and policy iteration
- Monte Carlo and temporal-difference learning
- Function approximation and deep Q-learning
- Policy gradients and actor–critic methods
Prerequisites: probability, Python programming