Abstract: In this lecture, we focus on a new online algorithm for vector balancing. Given any sequence of vectors, we first randomly and independently flip the signs of every vector. Then we design an online algorithm that discards only a small fraction of the signed vectors so that all partial sums of the remaining ones remain confined inside a given convex body. Combined with the partial coloring method (which we review), this algorithm proves weak forms of the Komlós conjecture. We will explain this simple randomized procedure and the natural geometric constant that controls its performance.