Hi everyone, I'm Julio Romano and I'm going to present you our work called Safe Online Bit Optimization with Roycon Strains. In this work we talk about digital advertising. There are some platforms as Google or Facebook with some advertising slots. And on the other side there are some advertisers who need to promote their product on such platforms. When a user opens a webpage, an auction is run and advertisers participate in the auction by bidding the maximum amount of money they are willing to spend for one click. Through an allocation rule, ads are assigned to slots. And then advertisers have to face some costs established by a payment rule. Usually advertisers have to fix the bid at each time instant that is one day. From the latest work in the literature, we can see that is empirically shown that some buyers in online advertising markets behave as if they are financially constrained and in particular as if they follow some right constraints. In fact, usually the advertiser Goh is a trade-off between achieving high volumes, that means high revenue, while maintaining high profitability that is measured through Roy Index. The work goal, therefore, is to suggest the optimal bid in strategy in order to maximize revenue while guaranteeing the satisfaction of Roy and budget constraint. This can be formulated as an optimization problem. We have an advertising campaign that is divided into capital and subcompane. Fixing a bid in strategy means fix a bid for each subcompane for each time instant. And the optimal bid in strategy must maximize the expected revenue, that is the objective function of the problem. Given by the value of one click, times the number of click received by bidding X. Then the optimization strategy must also satisfy the constraints. The peculiarity of this problem is that the number of click and cost functions are unknown a priori to the advertiser. Therefore such constraints are uncertain. Notice that nowadays most of the platforms do not provide any feature to force the satisfaction of these constraints. And therefore bid needs to develop bidding strategies that satisfy these uncertain constraints due to the learning process. In fact, we are going to learn number of click and cost function over time. Therefore we have to define the notion of pseudo-regretting in order to measure the learning policy performances and also the notion of safety. In this way, our goal is to minimize the pseudo-regret respecting the Roy and the budget constraints with high probability. The key point of our work is estimating the number of click and cost functions through Gaussian processes. And then, solving cyclically, the optimization problem with such approximated functions. Here we have some results. Last, we show that non-line learning algorithm can violate the budget or Roy constraints during the learning process less than a linear number of times while guaranteeing a sub-linear pseudo-regret. And this is the case of GCP algorithm, that means Gaussian combinatorial bandit. Therefore, we provide the GCP safe algorithm that on the other end guarantee with high probability the satisfaction of the constraints at the cost of a linear pseudo-regret. However, we show that a simple adaptation of GCP safe provides a sub-linear pseudo-regret when accepting a fixed tolerance in the constraints. GCP safe with tolerance is also safe with respect to the newly defined constraint. Finally, we experimentally evaluate our algorithms in a setting generated from real-world data. Thank you for listening.