Explore advanced concepts in convex optimization with Sebastien Bubeck from Microsoft Research in this comprehensive lecture. Delve into topics such as gradient oracles, the minimax principle and theorem, random oracles, and intuition behind antisymmetric lower bounds. Learn about general algorithms, inequalities, gradient queries, and efficient algorithms in the field of convex optimization. Gain valuable insights from this in-depth presentation, suitable for those with a strong background in optimization and mathematical analysis.