Piotr Krysta

Georgios Chionas, Olga Gorelkina, Piotr Krysta et al.

We study methods to enhance statistical privacy in blockchain transactions. We analyze economic mechanisms for privacy-aware transaction owners whose utility depends not only on the outcome of the mechanism but also negatively on the exposure of their economic preferences. First, we consider an order flow auction, where a user auctions off to specialized agents, called searchers, the right to execute her transaction while maintaining a degree of privacy. We examine how the degree of privacy affects the revenue of the auction and, broadly, the net utility of the privacy-aware user. In this new setting, we characterize the optimal auction, which is a sealed-bid auction. Subsequently, we analyze a variant of a Dutch auction in which the user gradually decreases the price and the degree of privacy until the transaction is sold. We compare the revenue of this auction to that of the optimal one as a function of the number of communication rounds. Then, we introduce a two-sided market - a privacy marketplace - with multiple users selling their transactions under their privacy preferences to multiple searchers. We propose a posted-price mechanism for the two-sided market that guarantees constant approximation of the optimal social welfare while maintaining incentive compatibility (from both sides of the market) and budget balance. This work builds on the emerging literature on privacy-preserving mechanism design, integrating statistical privacy guarantees into economic protocols to capture the impact of information leakage on blockchain users' utility.

Eleni Batziou, Georgios Birmpas, Georgios Chionas et al.

Sponsored search auctions are commonly modeled as an assignment of a fixed set of slots (positions) to a set of advertisers, with welfare maximization being reducible to a standard matching problem. Motivated by modern ad formats, we study a richer variant of the classical position auctions model, in which ads have heterogeneous sizes and the platform must jointly select and assign a subset of ads to positions subject to a global space constraint. We formulate this as a matching problem with a capacity constraint, and propose an algorithmic technique that goes beyond simple greedy methods while achieving constant factor approximation guarantees. Our allocation rule augments density-based ordering with capacity-aware local improvements, which allow for re-allocations that improve welfare, while respecting the capacity constraint. Applied in the context of position auctions, we analyze this mechanism under the assumption of single-parameter agents and position-dependent click-through-rates (CTRs). We show that a minor modification to our approach yields a universally truthful randomized mechanism with a constant factor approximation guarantee. To the best of our knowledge, this is the first truthful constant-approximation mechanism for this variant of capacity-constrained matching.

Dimitris Fotakis, Vasilis Kontonis, Piotr Krysta et al.

We introduce the problem of simultaneously learning all powers of a Poisson Binomial Distribution (PBD). A PBD of order $n$ is the distribution of a sum of $n$ mutually independent Bernoulli random variables $X_i$, where $\mathbb{E}[X_i] = p_i$. The $k$'th power of this distribution, for $k$ in a range $[m]$, is the distribution of $P_k = \sum_{i=1}^n X_i^{(k)}$, where each Bernoulli random variable $X_i^{(k)}$ has $\mathbb{E}[X_i^{(k)}] = (p_i)^k$. The learning algorithm can query any power $P_k$ several times and succeeds in learning all powers in the range, if with probability at least $1- δ$: given any $k \in [m]$, it returns a probability distribution $Q_k$ with total variation distance from $P_k$ at most $ε$. We provide almost matching lower and upper bounds on query complexity for this problem. We first show a lower bound on the query complexity on PBD powers instances with many distinct parameters $p_i$ which are separated, and we almost match this lower bound by examining the query complexity of simultaneously learning all the powers of a special class of PBD's resembling the PBD's of our lower bound. We study the fundamental setting of a Binomial distribution, and provide an optimal algorithm which uses $O(1/ε^2)$ samples. Diakonikolas, Kane and Stewart [COLT'16] showed a lower bound of $Ω(2^{1/ε})$ samples to learn the $p_i$'s within error $ε$. The question whether sampling from powers of PBDs can reduce this sampling complexity, has a negative answer since we show that the exponential number of samples is inevitable. Having sampling access to the powers of a PBD we then give a nearly optimal algorithm that learns its $p_i$'s. To prove our two last lower bounds we extend the classical minimax risk definition from statistics to estimating functions of sequences of distributions.