ML without tears

Category: Static optimization

  • Lagrangian multipliers, normal cones and KKT optimality conditions

    We consider constrained optimization problems of the kind: where the feasibility region is a polytope, i.e., is the set of such that: where are real matrices of size and , respectively, and are column vectors. Equivalently, we can rewrite (1) as: where are the -th row of and , respectively, and denotes the scalar product. In this post we…

  • Policy gradient for black-box optimization

    Policy gradient method are widely used in the Reinforcement Learning settings. In this post we build policy gradient from the ground up, starting from the easier static scenario first, where we maximize a reward function depending solely on our control variable . In subsequent posts, we will turn our attention to the contextual bandit setting,…