Optimizing Online Advertising with Multi-Armed Bandits: Mitigating the Cold Start Problem under Auction Dynamics

Online advertising platforms often face a common challenge: the cold start problem. Insufficient behavioral data (clicks) makes accurate click-through rate (CTR) forecasting of new ads challenging. CTR for "old" items can also be significantly underestimated due to their early performance influencing their long-term behavior on the platform. The cold start problem has far-reaching implications for businesses, including missed long-term revenue opportunities. To mitigate this issue, we developed a UCB-like algorithm under multi-armed bandit (MAB) setting for positional-based model (PBM), specifically tailored to auction pay-per-click systems. Our proposed algorithm successfully combines theory and practice: we obtain theoretical upper estimates of budget regret, and conduct a series of experiments on synthetic and real-world data that confirm the applicability of the method on the real platform. In addition to increasing the platform's long-term profitability, we also propose a mechanism for maintaining short-term profits through controlled exploration and exploitation of items.

Fast UCB-type algorithms for stochastic bandits with heavy and super heavy symmetric noise

In this study, we propose a new method for constructing UCB-type algorithms for stochastic multi-armed bandits based on general convex optimization methods with an inexact oracle. We derive the regret bounds corresponding to the convergence rates of the optimization methods. We propose a new algorithm Clipped-SGD-UCB and show, both theoretically and empirically, that in the case of symmetric noise in the reward, we can achieve an $O(\log T\sqrt{KT\log T})$ regret bound instead of $O\left (T^{\frac{1}{1+\alpha}} K^{\frac{\alpha}{1+\alpha}} \right)$ for the case when the reward distribution satisfies $\mathbb{E}_{X \in D}[|X|^{1+\alpha}] \leq \sigma^{1+\alpha}$ ($\alpha \in (0, 1])$, i.e. perform better than it is assumed by the general lower bound for bandits with heavy-tails. Moreover, the same bound holds even when the reward distribution does not have the expectation, that is, when $\alpha<0$.

Implicitly normalized forecaster with clipping for linear and non-linear heavy-tailed multi-armed bandits

The Implicitly Normalized Forecaster (INF) algorithm is considered to be an optimal solution for adversarial multi-armed bandit (MAB) problems. However, most of the existing complexity results for INF rely on restrictive assumptions, such as bounded rewards. Recently, a related algorithm was proposed that works for both adversarial and stochastic heavy-tailed MAB settings. However, this algorithm fails to fully exploit the available data. In this paper, we propose a new version of INF called the Implicitly Normalized Forecaster with clipping (INF-clip) for MAB problems with heavy-tailed reward distributions. We establish convergence results under mild assumptions on the rewards distribution and demonstrate that INF-clip is optimal for linear heavy-tailed stochastic MAB problems and works well for non-linear ones. Furthermore, we show that INF-clip outperforms the best-of-both-worlds algorithm in cases where it is difficult to distinguish between different arms.