In this paper, we studied the problem of contextual dynamic pricing where a seller sequentially prices goods based on contextual information. Buyers will purchase products only if the prices are below their valuations. The seller's goal is to design a pricing strategy to collect as much revenue as possible. 

We focused on two different settings characterised by the way in which the unknown valuation of the buyer depends on the given context. Initially, we assumed it to be a linear function further distorted by noise. We managed to design an algorithm that, under minor regularity assumptions, achieves an optimal regret bound of T^2/3, improving existing results. 

Then, we considered a generalization where the expected buyer valuation is a generic β-Hölder function of the context. For this model, our algorithm obtains a regret of T^(d+2β)/(d+3β), where d is the dimension of the context space. 

In this paper, we consider networked markets where a set of agents can participate with the double role of both buyers and sellers.

We begin by investigating the notion of stability in this setting, characterizing a well-defined subset of Nash equilibria that can be supported as competitive equilibria. We then establish convergence results toward Nash and competitive equilibria under various trading dynamics.                                                                      
Furthermore, we were interested in fairness concepts in this setting, for which we recovered several negative results: inessential agents always receive zero utility in any core outcome, and even essential agents can get zero utility in all core outcomes. 

Shilling is the use of artificial bids to make competition appear stronger and push prices upward. We study repeated first-price auctions in which shilling affects feedback but not allocation: the learner wins or loses against the real competing bid, but after a loss observes the maximum of the real bid and an independent shill bid. Thus the manipulation changes what the learner observes and hence how it learns to bid, without changing the outcome of the current auction. We analyze regret with respect to the best bid benchmark, assuming that the shill-bid distribution is known. Even then, shilling can mask the real bid, while useful side information appears only through intermittent low-shill events. Our algorithm combines a robust interval-elimination branch, which ignores the shilled report and achieves the dynamic-pricing rate O(T^{2/3}), with an optimistic branch that debiases losing-side reports and exploits the resulting suffix information when it is reliable and achieves the first-price auctions rate O(T^{1/2}). A validation and racing procedure lets the algorithm use these optimistic updates without knowing the right scale or feedback geometry in advance. We complement the upper bounds with a matching lower bound, up to logarithmic factors, in the single-active-region case. Overall, the results show that even feedback-only shilling can sharply alter the statistical difficulty of repeated bidding.

In this paper, we surveyed recent advances in the research about local differential privacy (LDP), with a particular focus on the remaining challenges faced by advertising companies as they transition to this new paradigm, prompted by the deprecation of third-party cookies in major browsers.

The introduction of LDP to obfuscate granular user data indeed creates a bottleneck for the digital advertising industry, as it prevents the use of standard machine learning pipelines to tackle the privacy/utility trade-off.  

Our work reviewed the main research directions that have been explored to cope with this issue, while trying to point out the main limitations of existing work. More specifically, we highlight the importance of conducting research works focusing on multi-task learning under LDP schemes and of seeking prior information to help design privacy-preserving mechanisms.

In Reinforcement Learning with Human Feedback, the goal is to define a policy that best matches users' preferences. In particular, rewards are never observed and are usually estimated on a human-labeled training set. Therefore, agents face a novel challenge: whether to undertake a costly process to update the reward model or to risk optimizing the policy with respect to an imprecise reward function. Motivated by this framework, we investigate the task of scheduling the optimal moments for model updates by framing it as a multi-armed bandit problem in which the agent can trigger a change in the distributions of the rewards of the arms. We analyze two settings representing two different effects that a model update can have on the rewards, and for both, provide algorithms and theoretical guarantees.