arXiv subjects

Stefano Leonardi

Publications and source records attributed to Stefano Leonardi.

At least 37 records · Page 2Linked to original sources

arXiv2023

Prophet Inequalities via the Expected Competitive Ratio

We consider prophet inequalities under downward-closed constraints. In this problem, a decision-maker makes immediate and irrevocable choices on arriving elements, subject to constraints. Traditionally, performance is compared to the expected offline optimum, called the \textit{Ratio of Expectations} (RoE). However, RoE has limitations as it only guarantees the average performance compared to the optimum, and might perform poorly against the realized ex-post optimal value. We study an alternative performance measure, the \textit{Expected Ratio} (EoR), namely the expectation of the ratio between algorithm's and prophet's value. EoR offers robust guarantees, e.g., a constant EoR implies achieving a constant fraction of the offline optimum with constant probability. For the special case of single-choice problems the EoR coincides with the well-studied notion of probability of selecting the maximum. However, the EoR naturally generalizes the probability of selecting the maximum for combinatorial constraints, which are the main focus of this paper. Specifically, we establish two reductions: for every constraint, RoE and the EoR are at most a constant factor apart. Additionally, we show that the EoR is a stronger benchmark than the RoE in that, for every instance (constraint and distribution), the RoE is at least a constant fraction of the EoR, but not vice versa. Both these reductions imply a wealth of EoR results in multiple settings where RoE results are known.

cs.GT↗

arXiv2023

Fair Division with Interdependent Values

We introduce the study of designing allocation mechanisms for fairly allocating indivisible goods in settings with interdependent valuation functions. In our setting, there is a set of goods that needs to be allocated to a set of agents (without disposal). Each agent is given a private signal, and his valuation function depends on the signals of all agents. Without the use of payments, there are strong impossibility results for designing strategyproof allocation mechanisms even in settings without interdependent values. Therefore, we turn to design mechanisms that always admit equilibria that are fair with respect to their true signals, despite their potentially distorted perception. To do so, we first extend the definitions of pure Nash equilibrium and well-studied fairness notions in literature to the interdependent setting. We devise simple allocation mechanisms that always admit a fair equilibrium with respect to the true signals. We complement this result by showing that, even for very simple cases with binary additive interdependent valuation functions, no allocation mechanism that always admits an equilibrium, can guarantee that all equilibria are fair with respect to the true signals.

cs.GT↗

arXiv2023

Repeated Bilateral Trade Against a Smoothed Adversary

We study repeated bilateral trade where an adaptive $σ$-smooth adversary generates the valuations of sellers and buyers. We provide a complete characterization of the regret regimes for fixed-price mechanisms under different feedback models in the two cases where the learner can post either the same or different prices to buyers and sellers. We begin by showing that the minimax regret after $T$ rounds is of order $\sqrt{T}$ in the full-feedback scenario. Under partial feedback, any algorithm that has to post the same price to buyers and sellers suffers worst-case linear regret. However, when the learner can post two different prices at each round, we design an algorithm enjoying regret of order $T^{3/4}$ ignoring log factors. We prove that this rate is optimal by presenting a surprising $T^{3/4}$ lower bound, which is the main technical contribution of the paper.

cs.LG↗

arXiv2023

Round-Robin Beyond Additive Agents: Existence and Fairness of Approximate Equilibria

Fair allocation of indivisible goods has attracted extensive attention over the last two decades, yielding numerous elegant algorithmic results and producing challenging open questions. The problem becomes much harder in the presence of strategic agents. Ideally, one would want to design truthful mechanisms that produce allocations with fairness guarantees. However, in the standard setting without monetary transfers, it is generally impossible to have truthful mechanisms that provide non-trivial fairness guarantees. Recently, Amanatidis et al. [2021] suggested the study of mechanisms that produce fair allocations in their equilibria. Specifically, when the agents have additive valuation functions, the simple Round-Robin algorithm always has pure Nash equilibria and the corresponding allocations are envy-free up to one good (EF1) with respect to the agents' true valuation functions. Following this agenda, we show that this outstanding property of the Round-Robin mechanism extends much beyond the above default assumption of additivity. In particular, we prove that for agents with cancelable valuation functions (a natural class that contains, e.g., additive and budget-additive functions), this simple mechanism always has equilibria and even its approximate equilibria correspond to approximately EF1 allocations with respect to the agents' true valuation functions. Further, we show that the approximate EF1 fairness of approximate equilibria surprisingly holds for the important class of submodular valuation functions as well, even though exact equilibria fail to exist!

cs.GT↗

arXiv2023

Fully Dynamic Online Selection through Online Contention Resolution Schemes

We study fully dynamic online selection problems in an adversarial/stochastic setting that includes Bayesian online selection, prophet inequalities, posted price mechanisms, and stochastic probing problems subject to combinatorial constraints. In the classical ``incremental'' version of the problem, selected elements remain active until the end of the input sequence. On the other hand, in the fully dynamic version of the problem, elements stay active for a limited time interval, and then leave. This models, for example, the online matching of tasks to workers with task/worker-dependent working times, and sequential posted pricing of perishable goods. A successful approach to online selection problems in the adversarial setting is given by the notion of Online Contention Resolution Scheme (OCRS), that uses a priori information to formulate a linear relaxation of the underlying optimization problem, whose optimal fractional solution is rounded online for any adversarial order of the input sequence. Our main contribution is providing a general method for constructing an OCRS for fully dynamic online selection problems. Then, we show how to employ such OCRS to construct no-regret algorithms in a partial information model with semi-bandit feedback and adversarial inputs.

cs.AI↗

arXiv2022

Truthful Matching with Online Items and Offline Agents

We study truthful mechanisms for welfare maximization in online bipartite matching. In our (multi-parameter) setting, every buyer is associated with a (possibly private) desired set of items, and has a private value for being assigned an item in her desired set. Unlike most online matching settings, where agents arrive online, in our setting the items arrive online in an adversarial order while the buyers are present for the entire duration of the process. This poses a significant challenge to the design of truthful mechanisms, due to the ability of buyers to strategize over future rounds. We provide an almost full picture of the competitive ratios in different scenarios, including myopic vs. non-myopic agents, tardy vs. prompt payments, and private vs. public desired sets. Among other results, we identify the frontier for which the celebrated $e/(e-1)$ competitive ratio for the vertex-weighted online matching of Karp, Vazirani and Vazirani extends to truthful agents and online items.

cs.GT↗

arXiv2022

Fair Equilibria in Sponsored Search Auctions: The Advertisers' Perspective

In this work we introduce a new class of mechanisms composed of a traditional Generalized Second Price (GSP) auction and a fair division scheme, in order to achieve some desired level of fairness between groups of Bayesian strategic advertisers. We propose two mechanisms, $β$-Fair GSP and GSP-EFX, that compose GSP with, respectively, an envy-free up to one item, and an envy-free up to any item fair division scheme. The payments of GSP are adjusted in order to compensate advertisers that suffer a loss of efficiency due the fair division stage. We investigate the strategic learning implications of the deployment of sponsored search auction mechanisms that obey to such fairness criteria. We prove that, for both mechanisms, if bidders play so as to minimize their external regret they are guaranteed to reach an equilibrium with good social welfare. We also prove that the mechanisms are budget balanced, so that the payments charged by the traditional GSP mechanism are a good proxy of the total compensation offered to the advertisers. Finally, we evaluate the quality of the allocations through experiments on real-world data.

cs.GT↗

arXiv2022

Stochastic dynamical wake modeling for wind farms

Low-fidelity analytical models of turbine wakes have traditionally been used for wind farm planning, performance evaluation, and demonstrating the utility of advanced control algorithms in increasing the annual energy production. In practice, however, it remains challenging to correctly estimate the flow and achieve significant performance gains using conventional low-fidelity models. This is due to the over-simplified static nature of wake predictions from models that are agnostic to the effects of atmospheric boundary layer turbulence and the complex aerodynamic interactions among wind turbines. To improve the predictive capability of low-fidelity models while remaining amenable to control design, we offer a stochastic dynamical modeling framework for capturing the effect of atmospheric turbulence on the thrust force and power generation as determined by the actuator disk concept. In this approach, we use stochastically forced linear models of the turbulent velocity field to augment the analytically computed wake velocity and achieve consistency with higher-fidelity models in capturing power and thrust force measurements. The power-spectral densities of our stochastic models are identified via convex optimization to ensure consistency with partially available velocity statistics or power and thrust force measurements while preserving model parsimony. We demonstrate the utility of our approach in capturing turbulence intensity variations behind wind turbines and estimating thrust force and power signals generated by large-eddy simulations of the flow over a cascade of turbines. Our results provide insight into the significance of sparse field measurements in recovering the statistical signature of wind farm turbulence using stochastic linear models.

physics.flu-dyn↗

arXiv2022

AI-based Data Preparation and Data Analytics in Healthcare: The Case of Diabetes

The Associazione Medici Diabetologi (AMD) collects and manages one of the largest worldwide-available collections of diabetic patient records, also known as the AMD database. This paper presents the initial results of an ongoing project whose focus is the application of Artificial Intelligence and Machine Learning techniques for conceptualizing, cleaning, and analyzing such an important and valuable dataset, with the goal of providing predictive insights to better support diabetologists in their diagnostic and therapeutic choices.

cs.LG↗

arXiv2021

Heat transfer increase by convection in liquid-infused surfaces for laminar and turbulent flows

Liquid-infused surfaces (LIS) can reduce friction drag in both laminar and turbulent flows. However, the heat transfer properties of such multi-phase surfaces have still not been investigated to a large extent. We use numerical simulations to study conjugate heat transfer of liquid-filled grooves. It is shown that heat transfer can increase for both laminar and turbulent liquid flows due to recirculation in the surface texture. For the increase to be substantial, the thermal conductivity of the solid must be similar to the thermal conductivity of the fluids, and the recirculation in the grooves must be sufficiently strong (Péclet number larger than 1). The ratio of the surface cavity to the system height is an upper limit of the direct contribution from the recirculation. While this ratio can be significant for laminar flows in microchannels, it is limited for turbulent flows, where the system scale (e.g. channel height) usually is much larger than the texture height. However, heat transfer enhancement on the order of $10\%$ is observed (with a net drag reduction) in a turbulent channel flow at a friction Reynolds number $Re_τ\approx 180$. It is shown that the turbulent convection in the bulk can be enhanced indirectly from the recirculation in the grooves.

physics.flu-dyn↗

arXiv2021

Distortion-Oblivious Algorithms for Minimizing Flow Time

We consider the classic online problem of scheduling on a single machine to minimize total flow time. In STOC 2021, the concept of robustness to distortion in processing times was introduced: for every distortion factor $μ$, an $O(μ^2)$-competitive algorithm $\operatorname{ALG}_μ$ which handles distortions up to $μ$ was presented. However, using that result requires one to know the distortion of the input in advance, which is impractical. We present the first \emph{distortion-oblivious} algorithms: algorithms which are competitive for \emph{every} input of \emph{every} distortion, and thus do not require knowledge of the distortion in advance. Moreover, the competitive ratios of our algorithms are $\tilde{O}(μ)$, which is a quadratic improvement over the algorithm from STOC 2021, and is nearly optimal (we show a randomized lower bound of $Ω(μ)$ on competitiveness).

cs.DS↗

arXiv2021

Bilateral Trade: A Regret Minimization Perspective

Bilateral trade, a fundamental topic in economics, models the problem of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold private valuations. In this paper, we cast the bilateral trade problem in a regret minimization framework over $T$ rounds of seller/buyer interactions, with no prior knowledge on their private valuations. Our main contribution is a complete characterization of the regret regimes for fixed-price mechanisms with different feedback models and private valuations, using as a benchmark the best fixed-price in hindsight. More precisely, we prove the following tight bounds on the regret: - $Θ(\sqrt{T})$ for full-feedback (i.e., direct revelation mechanisms). - $Θ(T^{2/3})$ for realistic feedback (i.e., posted-price mechanisms) and independent seller/buyer valuations with bounded densities. - $Θ(T)$ for realistic feedback and seller/buyer valuations with bounded densities. - $Θ(T)$ for realistic feedback and independent seller/buyer valuations. - $Θ(T)$ for the adversarial setting.

cs.GT↗

arXiv2021

Prophet Inequalities for Matching with a Single Sample

We consider the prophet inequality problem for (not necessarily bipartite) matching problems with independent edge values, under both edge arrivals and vertex arrivals. We show constant-factor prophet inequalities for the case where the online algorithm has only limited access to the value distributions through samples. First, we give a $16$-approximate prophet inequality for matching in general graphs under edge arrivals that uses only a single sample from each value distribution as prior information. Then, for bipartite matching and (one-sided) vertex arrivals, we show an improved bound of $8$ that also uses just a single sample from each distribution. Finally, we show how to turn our $16$-approximate single-sample prophet inequality into a truthful single-sample mechanism for online bipartite matching with vertex arrivals.

cs.DS↗

arXiv2021

Humans as Path-Finders for Safe Navigation

One of the most important barriers toward a widespread use of mobile robots in unstructured and human populated work environments is the ability to plan a safe path. In this paper, we propose to delegate this activity to a human operator that walks in front of the robot marking with her/his footsteps the path to be followed. The implementation of this approach requires a high degree of robustness in locating the specific person to be followed (the leader). We propose a three phase approach to fulfil this goal: 1. identification and tracking of the person in the image space, 2. sensor fusion between camera data and laser sensors, 3. point interpolation with continuous curvature curves. The approach is described in the paper and extensively validated with experimental results.

cs.RO↗

arXiv2021

Efficient Two-Sided Markets with Limited Information

A celebrated impossibility result by Myerson and Satterthwaite (1983) shows that any truthful mechanism for two-sided markets that maximizes social welfare must run a deficit, resulting in a necessity to relax welfare efficiency and the use of approximation mechanisms. Such mechanisms in general make extensive use of the Bayesian priors. In this work, we investigate a question of increasing theoretical and practical importance: how much prior information is required to design mechanisms with near-optimal approximations? Our first contribution is a more general impossibility result stating that no meaningful approximation is possible without any prior information, expanding the famous impossibility result of Myerson and Satterthwaite. Our second contribution is that one {\em single sample} (one number per item), arguably a minimum-possible amount of prior information, from each seller distribution is sufficient for a large class of two-sided markets. We prove matching upper and lower bounds on the best approximation that can be obtained with one single sample for subadditive buyers and additive sellers, regardless of computational considerations. Our third contribution is the design of computationally efficient blackbox reductions that turn any one-sided mechanism into a two-sided mechanism with a small loss in the approximation, while using only one single sample from each seller. On the way, our blackbox-type mechanisms deliver several interesting positive results in their own right, often beating even the state of the art that uses full prior information.

cs.GT↗

arXiv2021

Stochastic Bandits for Multi-platform Budget Optimization in Online Advertising

We study the problem of an online advertising system that wants to optimally spend an advertiser's given budget for a campaign across multiple platforms, without knowing the value for showing an ad to the users on those platforms. We model this challenging practical application as a Stochastic Bandits with Knapsacks problem over $T$ rounds of bidding with the set of arms given by the set of distinct bidding $m$-tuples, where $m$ is the number of platforms. We modify the algorithm proposed in Badanidiyuru \emph{et al.,} to extend it to the case of multiple platforms to obtain an algorithm for both the discrete and continuous bid-spaces. Namely, for discrete bid spaces we give an algorithm with regret $O\left(OPT \sqrt {\frac{mn}{B} }+ \sqrt{mn OPT}\right)$, where $OPT$ is the performance of the optimal algorithm that knows the distributions. For continuous bid spaces the regret of our algorithm is $\tilde{O}\left(m^{1/3} \cdot \min\left\{ B^{2/3}, (m T)^{2/3} \right\} \right)$. When restricted to this special-case, this bound improves over Sankararaman and Slivkins in the regime $OPT \ll T$, as is the case in the particular application at hand. Second, we show an $ Ω\left (\sqrt {m OPT} \right)$ lower bound for the discrete case and an $Ω\left( m^{1/3} B^{2/3}\right)$ lower bound for the continuous setting, almost matching the upper bounds. Finally, we use a real-world data set from a large internet online advertising company with multiple ad platforms and show that our algorithms outperform common benchmarks and satisfy the required properties warranted in the real-world application.

cs.GT↗

arXiv2021

Flow Time Scheduling with Uncertain Processing Time

We consider the problem of online scheduling on a single machine in order to minimize weighted flow time. The existing algorithms for this problem (STOC '01, SODA '03, FOCS '18) all require exact knowledge of the processing time of each job. This assumption is crucial, as even a slight perturbation of the processing time would lead to polynomial competitive ratio. However, this assumption very rarely holds in real-life scenarios. In this paper, we present the first algorithm for weighted flow time which do not require exact knowledge of the processing times of jobs. Specifically, we introduce the Scheduling with Predicted Processing Time (SPPT) problem, where the algorithm is given a prediction for the processing time of each job, instead of its real processing time. For the case of a constant factor distortion between the predictions and the real processing time, our algorithms match all the best known competitiveness bounds for weighted flow time -- namely $O(\log P), O(\log D)$ and $O(\log W)$, where $P,D,W$ are the maximum ratios of processing times, densities, and weights, respectively. For larger errors, the competitiveness of our algorithms degrades gracefully.

cs.DS↗

arXiv2021

Approximately Efficient Two-Sided Combinatorial Auctions

Mechanism design for one-sided markets has been investigated for several decades in economics and in computer science. More recently, there has been an increased attention on mechanisms for two-sided markets, in which buyers and sellers act strategically. For two-sided markets, an impossibility result of Myerson and Satterthwaite states that no mechanism can simultaneously satisfy individual rationality (IR), incentive compatibility (IC), strong budget-balance (SBB), and be efficient. On the other hand, important applications to web advertisement, stock exchange, and frequency spectrum allocation, require us to consider two-sided combinatorial auctions in which buyers have preferences on subsets of items, and sellers may offer multiple heterogeneous items. No efficient mechanism was known so far for such two-sided combinatorial markets. This work provides the first IR, IC and SBB mechanisms that provides an O(1)-approximation to the optimal social welfare for two-sided markets. An initial construction yields such a mechanism, but exposes a conceptual problem in the traditional SBB notion. This leads us to define the stronger notion of direct trade strong budget balance (DSBB). We then proceed to design mechanisms that are IR, IC, DSBB, and again provide an O(1)-approximation to the optimal social welfare. Our mechanisms work for any number of buyers with XOS valuations - a class in between submodular and subadditive functions - and any number of sellers. We provide a mechanism that is dominant strategy incentive compatible (DSIC) if the sellers each have one item for sale, and one that is bayesian incentive compatible (BIC) if sellers hold multiple items and have additive valuations over them. Finally, we present a DSIC mechanism for the case that the valuation functions of all buyers and sellers are additive.

cs.GT↗