Bandits with Knapsacks and predictions

We study the Bandits with Knapsacks problem with the aim of designing a learning-augmented online learning algorithm upholding better regret guarantees than the state-of-the-art primal-dual algorithms with worst-case guarantees, under both stochastic and adversarial inputs. In the adversarial case, we obtain better competitive ratios when the input predictions are accurate, while also maintaining worst-case guarantees for imprecise predictions. We introduce two algorithms tailored for the full and bandit feedback settings, respectively. Both algorithms integrate a static prediction with a worst-case no-α-regret algorithm. This yields an optimized competitive ratio of (π + (1 - π)/α)^-1 in scenarios where the prediction is perfect, and a competitive ratio of α/(1 - π) in the case of highly imprecise predictions, where π ∈ (0, 1) is chosen by the learner and α is Slater's parameter. We complement this analysis by studying the stochastic setting under full feedback. We provide an algorithm which guarantees a pseudo-regret of Õ(√T) with poor predictions, and 0 pseudo-regret with perfect predictions.