We study the fair allocation of indivisible items to groups of agents from the perspectives of both the agents and a centralized allocator. In our setting, the centralized allocator aims to ensure that the allocation is fair both among the groups and between individual agents. This setting applies to many real-world scenarios, such as when a school administrator allocates resources (e.g., office spaces and supplies) to staff members within departments or when a city council allocates limited housing units to families in need across different communities. To ensure fairness between agents, we consider the classical notion of envy-freeness (EF). To ensure fairness among groups, we introduce the notion of centralized group equitability (CGEQ), which captures fairness for groups from the centralized allocator’s perspective. Because an EF or CGEQ allocation does not always exist in general, we consider their natural relaxations: envy-freeness to one item (EF1) and centralized group equitability up to one item (CGEQ1). For different classes of valuation functions of the agents and the centralized allocator, we show that allocations satisfying both EF1 and CGEQ1 always exist, and we design efficient algorithms to compute such allocations. We also consider the centralized group maximin share (CGMMS) from the centralized allocator's perspective as a group-level fairness objective with EF1 for agents, and present several results.

We consider a general non-stochastic online pricing bandit setting in a procurement scenario where a buyer with a budget wants to procure items from a fixed set of sellers to maximize the buyer's reward by dynamically offering purchasing prices to the sellers, where the sellers' costs and values at each time period can change arbitrarily and the sellers determine whether to accept the offered prices to sell the items. This setting models online pricing scenarios of procuring resources or services in multi-agent systems. We first consider the offline setting when sellers' costs and values are known in advance and investigate the best fixed-price policy in hindsight. We show that it has a tight approximation guarantee with respect to the offline optimal solutions. In the general online setting, we propose an online pricing policy, Granularity-based Pricing (GAP), which exploits underlying side-information from the feedback graph when the budget is given as the input. We show that GAP achieves an upper bound of O(n{v_{max}}{c_{min}}sqrt{B/c_{min}}ln B) on the alpha-regret where n, v_{max}, c_{min}, and B are the number, the maximum value, the minimum cost of sellers, and the budget, respectively. We then extend it to the unknown budget case by developing a variant of GAP, namely Doubling-GAP, and show its alpha-regret is at most O(n{v_{max}}{c_{min}}sqrt{B/c_{min}}ln2 B). We also provide an alpha-regret lower bound Omega(v_{max}sqrt{Bn/c_{min}}) of any online policy that is tight up to sub-linear terms. We conduct simulation experiments to show that the proposed policy outperforms the baseline algorithms.

Man-made and natural disruptions such as planned constructions on roads, suspensions of bridges, and blocked roads by trees/mudslides/floods can often create obstacles that separate two connected regions. As a result, the traveling and reachability of agents from their respective regions to other regions can be affected. To minimize the impact of the obstacles and maintain agent accessibility, we initiate the problem of constructing a new pathway (e.g., a detour or new bridge) connecting the regions disconnected by obstacles from the mechanism design perspective. In the problem, each agent in their region has a private location and is required to access the other region. The cost of an agent is the distance from their location to the other region via the pathway. Our goal is to design strategyproof mechanisms that elicit truthful locations from the agents and approximately optimize the social or maximum cost of agents by determining locations in the regions for building a pathway. We provide a characterization of all strategyproof and anonymous mechanisms. For the social and maximum costs, we provide upper and lower bounds on the approximation ratios of strategyproof mechanisms.

We study the k-facility location games with optional preferences on the line. In the games, each strategic agent has a public location preference on the k facility locations and a private optional preference on the preferred/acceptable set of facilities out of the k facilities. Our goal is to design strategyproof mechanisms to elicit agents’ optional preferences and locate k facilities to minimize the social or maximum cost of agents based on their facility preferences and public agent locations. We consider two variants of the facility location games with optional preferences: the Min variant and the Max variant where the agent’s cost is defined as their distance to the closest acceptable facility and the farthest acceptable facility, respectively. For the Min variant, we present two deterministic strategyproof mechanisms to minimize the maximum cost and social cost with k ≥ 3 facilities, achieving approximation ratios of 3 and 2n+1 respectively. We complement the results by establishing lower bounds of 3/2 and n/4 for the approximation ratios achievable by any deterministic strategyproof mechanisms for the maximum cost and social cost, respectively. We then improve our results in a special setting of the Min variant where there are exactly three facilities and present two deterministic strategyproof mechanisms to minimize the maximum cost and social cost. For the Max variant, we present an optimal deterministic strategyproof mechanism for the maximum cost and a k-approximation deterministic strategyproof mechanism for the social cost.

We study the mechanism design problem of facility location on a metric space in the learning-augmented framework, where mechanisms have access to an imperfect prediction of optimal facility locations. Our goal is to design strategyproof (SP) mechanisms to elicit agent preferences on the facility locations truthfully and, leveraging the given imperfect prediction, determine the facility location that approximately minimizes the maximum cost among all agents. In particular, we seek SP mechanisms whose approximation guarantees depend on the prediction errors — achieve improved guarantees when the prediction is accurate (known as the consistency), while still ensuring robust worst-case performance when the prediction is arbitrarily inaccurate (known as the robustness). When the metric space is the real line, we characterize all deterministic SP mechanisms with consistency strictly less than 2 and bounded robustness: such mechanisms must be the MinMaxP mechanism, which returns the prediction location if it lies between the two extreme agent locations and, otherwise, returns the closest agent location to the prediction. We further show that, for any prediction error η ≥ 0, while MinMaxP is (1 + min(1, η))-approximation, no deterministic SP mechanism can achieve a better approximation. In two-dimensional spaces with the l_p metric, we analyze the approximation guarantees of a deterministic mechanism that runs MinMaxP independently on each coordinate, as well as a randomized mechanism that selects between two deterministic ones with specific probabilities. Finally, we discuss the group strategyproofness of the considered mechanisms.

We consider the k-facility location problems with capacity constraints in bounded location space from the mechanism design perspective. In this problem, we seek to locate k capacity constrained facilities in a bounded interval (i.e., B=[bl,br]) to serve agents, who have preferences on the ideal locations of the facilities in the interval. Our goal is to design strategyproof mechanisms to elicit agents’ true ideal locations and locate facilities that minimize the social cost and maximum cost, which are defined to be the sum and the maximum of the agents’ costs (i.e., agents’ distances to their facilities), respectively. For the equal capacity setting without spare capacity (i.e., all the agents can be served exactly), we provide a deterministic strategyproof mechanism. For any bounded interval (i.e., bl, br∈R), our mechanism has approximation ratios of n-1 for the social cost and 4 for the maximum cost with k≥3 facilities and n≥3 agents. We also establish lower bounds of n/2 for the social cost by a common class of deterministic mechanisms that order agents from left to right, and 2 for the maximum cost by any deterministic mechanism. Our mechanism also achieves tight bounds for both costs with k<3 facilities. We then consider the equal capacity setting with spare capacity and the arbitrary capacity setting without spare capacity. For these two settings and any bounded interval, we provide randomized strategyproof mechanisms with approximation ratios of n/2 for the social cost and 2 for the maximum cost with any number of facilities. We complement this result by establishing lower bounds of 5/3 for the social cost and 3/2 for the maximum cost.

Longitudinal human behavior modeling has received increasing attention over the years due to its widespread applications to patient monitoring, dietary and lifestyle recommendations, and just-in-time intervention for at-risk individuals (e.g., problematic drug users and struggling students), to name a few. Using in-the-moment health data collected via ubiquitous devices (e.g., smartphones and smartwatches), this multidisciplinary field focuses on developing predictive models for certain health or well-being outcomes (e.g., depression and stress) in the short future given the time series of individual behaviors (e.g., resting heart rate, sleep quality, and current feelings). Yet, most existing models on these data, which we refer to as ubiquitous health data, do not achieve adequate accuracy. The latest works that yielded promising results have yet to consider realistic aspects of ubiquitous health data (e.g., containing features of different types and high rate of missing values) and the consumption of various resources (e.g., computing power, time, and cost). Given these two shortcomings, it is dubious whether these studies could translate to realistic settings. In this paper, we propose MuHBoost, a multi-label boosting method for addressing these shortcomings, by leveraging advanced methods in large language model (LLM) prompting and multi-label classification (MLC) to jointly predict multiple health or well-being outcomes. Because LLMs can hallucinate when tasked with answering multiple questions simultaneously, we also develop two variants of MuHBoost that alleviate this issue and thereby enhance its predictive performance. We conduct extensive experiments to evaluate MuHBoost and its variants on 13 health and well-being prediction tasks defined from four realistic ubiquitous health datasets. Our results show that our three developed methods outperform all considered baselines across three standard MLC metrics, demonstrating their effectiveness while ensuring resource efficiency.

We introduce and analyze distance preservation games (DPGs). In DPGs, agents express ideal distances to other agents and need to choose locations in the unit interval while preserving their ideal distances as closely as possible. We analyze the existence and computation of location profiles that are jump stable (i.e., no agent can benefit by moving to another location) or welfare optimal for DPGs, respectively. Specifically, we prove that there are DPGs without jump stable location profiles and identify important cases where such outcomes always exist and can be computed efficiently. Similarly, we show that finding welfare optimal location profiles is NP-complete and present approximation algorithms for finding solutions with social welfare close to optimal. Finally, we prove that DPGs have a price of anarchy of at most 2.

Aggregate games model interdependent decision making when an agent’s utility depends on their own choice and the aggregation of everyone’s choices. We define a compactly representable subclass of aggregate games we call additive aggregate games, which encompasses popular games like congestion games, anonymous games, Schelling games, etc. We study computational questions on pure Nash equilibrium (PNE) and pure strong Nash equilibrium (SNE). We show that PNE existence is NP-complete for very simple cases of additive aggregate games. We devise an efficient algorithmic scheme for deciding the existence of a PNE and computing one (if it exists) for bounded aggregate space. We also give an approximation algorithm for a special type of additive aggregate games. For SNE, we show that SNE recognition is co-NP-complete and SNE existence is $\Sigma^P_2$-complete, even for simple types of additive aggregate games. For broad classes, we provide several novel and efficient aggregate-space algorithms for recognizing an SNE and deciding the existence of an SNE. Finally, we connect our results to several popular classes of games and show how our computational schemes can shed new light on these games.

In this paper, we propose a new approach to train deep learning models using game theory concepts including Generative Adversarial Networks (GANs) and Adversarial Training (AT) where we deploy a double-oracle framework using best response oracles. GAN is essentially a two-player zero-sum game between the generator and the discriminator. The same concept can be applied to AT with attacker and classifier as players. Training these models is challenging as a pure Nash equilibrium may not exist and even finding the mixed Nash equilibrium is difficult as training algorithms for both GAN and AT have a large-scale strategy space. Extending our preliminary model DO-GAN, we propose the methods to apply the double oracle framework concept to Adversarial Neural Architecture Search (NAS for GAN) and Adversarial Training (NAS for AT) algorithms. We first generalize the players' strategies as the trained models of generator and discriminator from the best response oracles. We then compute the meta-strategies using a linear program. For scalability of the framework where multiple network models of best responses are stored in the memory, we prune the weakly-dominated players' strategies to keep the oracles from becoming intractable. Finally, we conduct experiments on MNIST, CIFAR-10 and TinyImageNet for DONAS-GAN. We also evaluate the robustness under FGSM and PGD attacks on CIFAR-10, SVHN and TinyImageNet for DONAS-AT. We show that all our variants have significant improvements in both subjective qualitative evaluation and quantitative metrics, compared with their respective base architectures.

We study the group-fair obnoxious facility location problems from the mechanism design perspective where agents belong to different groups and have private location preferences on the undesirable locations of the facility. Our main goal is to design strategyproof mechanisms that elicit the true location preferences from the agents and determine a facility location that approximately optimizes several group-fair objectives. We first consider the maximum total and average group cost (group-fair) objectives. For these objectives, we propose deterministic mechanisms that achieve 3-approximation ratios and provide matching lower bounds. We then provide the characterization of 2-candidate strategyproof randomized mechanisms. Leveraging the characterization, we design randomized mechanisms with improved approximation ratios of 2 for both objectives. We also provide randomized lower bounds of 5/4 for both objectives. Moreover, we investigate intergroup and intragroup fairness (IIF) objectives, addressing fairness between groups and within each group. We present a mechanism that achieves a 4-approximation for the IIF objectives and provide tight lower bounds.

We study the facility location problems (FLPs) with altruistic agents who act to benefit others in their affiliated groups. Our aim is to design mechanisms that elicit true locations from the agents in different overlapping groups and place a facility to serve agents to approximately optimize a given objective based on agents' costs to the facility. Existing studies of FLPs consider myopic agents who aim to minimize their own costs to the facility. We mainly consider altruistic agents with well-motivated group costs that are defined over costs incurred by all agents in their groups. Accordingly, we define Pareto strategyproofness to account for altruistic agents and their multiple group memberships with incomparable group costs. We consider mechanisms satisfying this strategyproofness under various combinations of the planner's objectives and agents' group costs. For each of these settings, we provide upper and lower bounds of approximation ratios of the mechanisms satisfying Pareto strategyproofness.

We study a variation of facility location problems (FLPs) that aims to improve the accessibility of agents to the facility within the context of mechanism design without money. In such a variation, agents have preferences on the ideal locations of the facility on a real line, and the facility’s location is fixed in advance where (re)locating the facility is not possible due to various constraints (e.g., limited space and construction costs). To improve the accessibility of agents to facilities, existing mechanism design literature in FLPs has proposed to structurally modify the real line (e.g., by adding a new interval) or provide shuttle services between two points when structural modifications are not possible. In this paper, we focus on the latter approach and propose to construct an accessibility range to extend the accessibility of the facility. In the range, agents can receive accommodations (e.g., school buses, campus shuttles, or pickup services) to help reach the facility. Therefore, the cost of each agent is the distance from their ideal location to the facility (possibility) through the range. We focus on designing strategyproof mechanisms that elicit true ideal locations from the agents and construct accessibility ranges (intervals) to approximately minimize the social cost or the maximum cost of agents. For both social and maximum costs, we design group strategyproof mechanisms and strong group strategyproof mechanisms with (asymptotically) tight bounds on the approximation ratios.

Decision-making problems, categorized as single-agent, e.g., Atari, cooperative multi-agent, e.g., Hanabi, competitive multi-agent, e.g., Hold'em poker, and mixed cooperative and competitive, e.g., football, are ubiquitous in the real world. Although various methods have been proposed to address the specific decision-making categories, these methods typically evolve independently and cannot generalize to other categories. Therefore, a fundamental question for decision-making is: *Can we develop **a single algorithm** to tackle **ALL** categories of decision-making problems?* There are several main challenges to address this question: i) different decision-making categories involve different numbers of agents and different relationships between agents, ii) different categories have different solution concepts and evaluation measures, and iii) there lacks a comprehensive benchmark covering all the categories. This work presents a preliminary attempt to address the question with three main contributions. i) We propose the generalized mirror descent (GMD), a generalization of MD variants, which considers multiple historical policies and works with a broader class of Bregman divergences. ii) We propose the configurable mirror descent (CMD) where a meta-controller is introduced to dynamically adjust the hyper-parameters in GMD conditional on the evaluation measures. iii) We construct the GameBench with 15 academic-friendly games across different decision-making categories. Extensive experiments demonstrate that CMD achieves empirically competitive or better outcomes compared to baselines while providing the capability of exploring diverse dimensions of decision making.

We present algorithms of two flavors{—}one rooted in constraint satisfaction problems (CSPs) and the other in learning dynamics{—}to compute pure-strategy Nash equilibrium (PSNE) in k-dimensional congestion games (k-DCGs) and their variants. The two algorithmic approaches are driven by whether or not a PSNE is guaranteed to exist. We first show that deciding the existence of a PSNE in a k-DCG is NP-complete even when players have binary and unit demand vectors. For general cost functions (potentially non-monotonic), we devise a new CSP-inspired algorithmic framework for PSNE computation, leading to algorithms that run in polynomial time under certain assumptions while offering exponential savings over standard CSP algorithms. We further refine these algorithms for variants of k-DCGs. Our experiments demonstrate the effectiveness of this new CSP framework for hard, non-monotonic k-DCGs. We then provide learning dynamics-based PSNE computation algorithms for linear and exponential cost functions. These algorithms run in polynomial time under certain assumptions. For general cost, we give a learning dynamics algorithm for an (\ensuremath{(\alpha, \beta)})-approximate PSNE (for certain \ensuremath{\alpha} and \ensuremath{\beta}). Lastly, we also devise polynomial-time algorithms for structured demands and cost functions.

We study various models for the one-dimensional multi-stage facility location problems with transient agents, where a transient agent arrives in some stage and stays for a number of consecutive stages. In the problems, we need to serve each agent in one of their stages by determining the location of the facility at each stage. In the first model, we assume there is no cost for moving the facility across the stages. We focus on optimal algorithms to minimize both the social cost objective, defined as the total distance of all agents to the facility over all stages, and the maximum cost objective, defined as the max distance of any agent to the facility over all stages. For each objective, we give a slice-wise polynomial (XP) algorithm (i.e., solvable in m^f(k) for some fixed parameter k and computable function f, where m is the input size) and show that there is a polynomial-time algorithm when a natural first-come-first-serve (FCFS) order of agent serving is enforced. We then consider the mechanism design problem, where the agents' locations and arrival stages are private, and design a group strategy-proof mechanism that achieves good approximation ratios for both objectives and settings with and without FCFS ordering. In the second model, we consider the facility's moving cost between adjacent stages under the social cost objective, which accounts for the total moving distance of the facility. Correspondingly, we design XP (and polynomial time) algorithms and a group strategy-proof mechanism for settings with or without the FCFS ordering.

We consider a sequential blocked matching (SBM) model where strategic agents repeatedly report ordinal preferences over a set of services to a central planner. The planner's goal is to elicit agents' true preferences and design a policy that matches services to agents in order to maximize the expected social welfare with the added constraint that each matched service can be blocked or unavailable for a number of time periods. Naturally, SBM models the repeated allocation of reusable services to a set of agents where each allocated service becomes unavailable for a fixed duration. We first consider the offline SBM setting, where the strategic agents are aware of their true preferences. We measure the performance of any policy by distortion, the worst-case multiplicative approximation guaranteed by any policy. For the setting with s services, we establish lower bounds of Ω(s) and Ω(√s) on the distortions of any deterministic and randomised mechanisms, respectively. We complement these results by providing approximately truthful, measured by incentive ratio, deterministic and randomised policies based on random serial dictatorship which match our lower bounds. Our results show that there is a significant improvement if one considers the class of randomised policies. Finally, we consider the online SBM setting with bandit feedback where each agent is initially unaware of her true preferences, and the planner must facilitate each agent in the learning of their preferences through the matching of services over time. We design an approximately truthful mechanism based on the explore-then-commit paradigm, which achieves logarithmic dynamic approximate regret.

The cross-fertilization of AI and economic concepts has led to the advanced development of novel computational ideas. These ideas include models and approaches for analyzing multi-agent interaction (via game-theoretic models and solution concepts) in strategic environments and designing strategic environments (via mechanism design) to address principal decision-making problems involving multi-agent within various social contexts. In what follows, we will discuss our works on these two main topics. For analyzing multi-agent interaction, we will discuss several computational game-theoretic models to capture various agent characteristics and social (e.g., self-organization) domains. For designing strategic environments, we will discuss principal decision-making mechanism design settings in various social (e.g., facility location) contexts where the principal has to design mechanisms that elicit agent preferences over social outcomes and implement the principal's desirable social outcomes.

We study the facility location problems where agents are located on a real line and divided into groups based on criteria such as ethnicity or age. Our aim is to design mechanisms to locate a facility to approximately minimize the costs of groups of agents to the facility fairly while eliciting the agents' locations truthfully. We first explore various well-motivated group fairness cost objectives for the problems and show that many natural objectives have an unbounded approximation ratio. We then consider minimizing the maximum total group cost and minimizing the average group cost objectives. For these objectives, we show that existing classical mechanisms (e.g., median) and new group-based mechanisms provide bounded approximation ratios, where the group-based mechanisms can achieve better ratios. We also provide lower bounds for both objectives. To measure fairness between groups and within each group, we study a new notion of intergroup and intragroup fairness (IIF) . We consider two IIF objectives and provide mechanisms with tight approximation ratios.

A preference profile is single-peaked on a tree if the candidate set can be equipped with a tree structure so that the preferences of each voter are decreasing from their top candidate along all paths in the tree. This notion was introduced by Demange (1982), and subsequently Trick (1989b) described an efficient algorithm for deciding if a given profile is single-peaked on a tree. We study the complexity of multiwinner elections under several variants of the Chamberlin–Courant rule for preferences single-peaked on trees. We show that in this setting the egalitarian version of this rule admits a polynomial-time winner determination algorithm. For the utilitarian version, we prove that winner determination remains NP-hard for the Borda scoring function; indeed, this hardness results extends to a large family of scoring functions. However, a winning committee can be found in polynomial time if either the number of leaves or the number of internal vertices of the underlying tree is bounded by a constant. To benefit from these positive results, we need a procedure that can determine whether a given profile is single-peaked on a tree that has additional desirable properties (such as, e.g., a small number of leaves). To address this challenge, we develop a structural approach that enables us to compactly represent all trees with respect to which a given profile is single-peaked. We show how to use this representation to efficiently find the best tree for a given profile for use with our winner determination algorithms: Given a profile, we can efficiently find a tree with the minimum number of leaves, or a tree with the minimum number of internal vertices among trees on which the profile is single-peaked. We then explore the power and limitations of this framework: we develop polynomial-time algorithms to find trees with the smallest maximum degree, diameter, or pathwidth, but show that it is NP-hard to check whether a given profile is single-peaked on a tree that is isomorphic to a given tree, or on a regular tree.

We study the problem faced by a decision maker who wants to locate a set of facilities on a real line and allocate agents/items to the facilities. The items have given locations on the line, and can only be assigned to one of their closest facilities. The facilities are controlled by managers, who have additive utility over the items. An optimal solution that maximizes the (utilitarian or egalitarian) social welfare of the facilities may present a very unbalanced allocation of the items to the facilities and hence be perceived as unfair. In this paper, we are interested in fair allocation among facility managers and consider the well-studied proportionality and envy-freeness fairness notions and their relaxations. We assess the availability, existence, approximability, and the quality (price of fairness) of fair solutions, where the quality measures the system efficiency loss under a fair allocation compared to the one that maximizes the social welfare. Further, we show that one can find a Pareto-optimal solution in polynomial time.

The study of approximate mechanism design for facility location has been in the center of research at the intersection of artificial intelligence and economics for the last decade, largely due to its practical importance in various domains, such as social planning and clustering. At a high level, the goal is to select a number of locations on which to build a set of facilities, aiming to optimize some social objective based on the preferences of strategic agents, who might have incentives to misreport their private information. This paper presents a comprehensive survey of the significant progress that has been made since the introduction of the problem, highlighting all the different variants and methodologies, as well as the most interesting directions for future research.

In this paper, we consider the problem of designing budget-feasible mechanisms for selecting agents with private costs from various groups to ensure proportional representation, where the minimum proportion of the selected agents from each group is maximized. Depending on agents' membership in the groups, we consider two main models: single group setting where each agent belongs to only one group, and multiple group setting where each agent may belong to multiple groups. We propose novel budget-feasible proportion-representative mechanisms for these models, which can select representative agents from different groups. The proposed mechanisms guarantee theoretical properties of individual rationality, budget-feasibility, truthfulness, and approximation performance on proportional representation.

Public projects can succeed or fail for many reasons such as the feasibility of the original goal and coordination among contributors. One major reason for failure is that insufficient work leaves the project partially completed. For certain types of projects anything short of full completion is a failure (e.g., feature request on software projects in GitHub). Therefore, project success relies heavily on individuals allocating sufficient effort. When there are multiple public projects, each contributor needs to make decisions to best allocate his/her limited effort (e.g., time) to projects while considering the effort allocation decisions of other strategic contributors and his/her parameterized utilities based on values and costs for the projects. In this paper, we introduce a game-theoretic effort allocation model of contributors to public projects for modeling effort allocation of strategic contributors. We study the related Nash equilibrium (NE) computational problems and provide NP-hardness results for the existence of NE and polynomial-time algorithms for finding NE in restricted settings. Finally, we investigate the inefficiency of NE measured by the price of anarchy and price of stability.

We introduce the problem of maximizing approximately $k$-submodular functions subject to size constraints. In this problem, one seeks to select $k$-disjoint subsets of a ground set with bounded total size or individual sizes, and maximum utility, given by a function that is "close" to being $k$-submodular. The problem finds applications in tasks such as sensor placement, where one wishes to install $k$ types of sensors whose measurements are noisy, and influence maximization, where one seeks to advertise $k$ topics to users of a social network whose level of influence is uncertain. To deal with the problem, we first provide two natural definitions for approximately $k$-submodular functions and establish a hierarchical relationship between them. Next, we show that simple greedy algorithms offer approximation guarantees for different types of size constraints. Last, we demonstrate experimentally that the greedy algorithms are effective in sensor placement and influence maximization problems.

We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the corresponding optimization problem, where the goal is to locate facilities to minimize either the total cost to all agents or the maximum cost of any agent is NP-hard. However, we show that the problem is fixed-parameter tractable, and the optimal solution can be computed in polynomial time whenever the number of facilities is bounded, or when all facilities have identical capacities. We then consider the problem from a mechanism design perspective where the agents are strategic and need not reveal their true locations. We show that several natural mechanisms studied in the uncapacitated setting either lose strategyproofness or a bound on the solution quality %on the returned solution for the total or maximum cost objective. We then propose new mechanisms that are strategyproof and achieve approximation guarantees that almost match the lower bounds.

Standard disaster response involves using drones (or helicopters) for reconnaissance and using people on the ground to mitigate the damage. In this paper, we look at the problem of wildfires and propose an efficient resource allocation strategy to cope with both dynamically changing environment and uncertainty. In particular, we propose Firefly, a new resource allocation algorithm, that can provably achieve optimal or near optimal solutions with high probability by first efficiently allocating observation drones to collect information to reduce uncertainty, and then allocate the firefighting units to extinguish fire. For the former, Firefly uses a combination of maximum set coverage formulation and a novel utility estimation technique, and it uses a knapsack formulation to calculate the allocation for the latter. We also demonstrate empirically by using a real-world dataset that Firefly achieves up to 80-90% performance of the offline optimal solution, even with a small amount of drones, in most of the cases.

We consider a general adversarial multi-armed blocking bandit setting where each played arm can be blocked (unavailable) for some time periods and the reward per arm is given at each time period adversarially without obeying any distribution. The setting models scenarios of allocating scarce limited supplies (e.g., arms) where the supplies replenish and can be reused only after certain time periods. We first show that, in the optimization setting, when the blocking durations and rewards are known in advance, finding an optimal policy (e.g., determining which arm per round) that maximises the cumulative reward is strongly NP-hard, eliminating the possibility of a fully polynomial-time approximation scheme (FPTAS) for the problem unless P = NP. To complement our result, we show that a greedy algorithm that plays the best available arm at each round provides an approximation guarantee that depends on the blocking durations and the path variance of the rewards. In the bandit setting, when the blocking durations and rewards are not known, we design two algorithms, RGA and RGA-META, for the case of bounded duration an path variation. In particular, when the variation budget BT is known in advance, RGA can achieve O(\sqrt{T(2\tilde{D}+K)B{T}}) dynamic approximate regret. On the other hand, when B_T is not known, we show that the dynamic approximate regret of RGA-META is at most O((K+\tilde{D})^{1/4}\tilde{B}^{1/2}T^{3/4}) where \tilde{B} is the maximal path variation budget within each batch of RGA-META (which is provably in order of o(\sqrt{T}). We also prove that if either the variation budget or the maximal blocking duration is unbounded, the approximate regret will be at least Theta(T). We also show that the regret upper bound of RGA is tight if the blocking durations are bounded above by an order of O(1).

We initiate the study of indivisible chore allocation for agents with asymmetric shares. The fairness concept we focus on is the weighted natural generalization of maxmin share: WMMS fairness and OWMMS fairness. We first highlight the fact that commonly-used algorithms that work well for allocation of goods to asymmetric agents, and even for chores to symmetric agents do not provide good approximations for allocation of chores to asymmetric agents under WMMS. As a consequence, we present a novel polynomial-time constant-approximation algorithm, via linear program, for OWMMS. For two special cases: the binary valuation case and the 2-agent case, we provide exact or better constant-approximation algorithms.

We study envy-free allocations of indivisible goods to agents in settings where each agent is unaware of the bundles (or allocated goods) of other agents. In particular, we propose maximin aware (MMA) fairness measure, which guarantees that every agent, given the bundle allocated to her, is aware that she does not get the worst bundle, even if she does not know how the other goods are distributed. We also introduce two of its relaxations, MMA1 and MMAX. We show that MMA1 and MMAX potentially have stronger egalitarian guarantees than EF1 and are easier to achieve than MMS and EFX. Finally, we present a polynomial-time algorithm, which computes an allocation such that every agent is either 1/2-approximate MMA or exactly MMAX. Interestingly, the returned allocation is also 1/2-approximate EFX when all agents have subadditive valuations, which answers an open question left in [Plaut and Roughgarden, SODA 2018].

Due to the recent cyber attacks, cybersecurity is becoming more critical in modern society. A single attack (e.g., WannaCry ransomware attack) can cause as much as $4 billion in damage. However, the cybersecurity investment by companies is far from satisfactory. Therefore, governments (e.g., in the UK) launch grants and subsidies to help companies to boost their cybersecurity to create a safer national cyber environment. The allocation problem is hard due to limited subsidies and the interdependence between self-interested companies and the presence of a strategic cyber attacker. To tackle the government's allocation problem, we introduce a Stackelberg game-theoretic model where the government first commits to an allocation and the companies/users and attacker simultaneously determine their protection and attack (pure or mixed) strategies, respectively. For the pure-strategy case, while there may not be a feasible allocation in general, we prove that computing an optimal allocation is NP-hard and propose a linear reverse convex program when the attacker can attack all users. For the mixed-strategy case, we show that there is a polynomial time algorithm to find an optimal allocation when the attacker has a single-attack capability. We then provide a heuristic algorithm, based on best-response-gradient dynamics, to find an effective allocation in the general setting. Experimentally, we show that our heuristic is effective and outperforms other baselines on synthetic and real data.

There are over 1 million homeless youth in the U.S. each year. To reduce homelessness, U.S. Housing and Urban Development (HUD) and housing communities provide housing programs/services to homeless youth with the goal of improving their long-term situation. Housing communities are facing a difficult task of filling their housing programs, with as many youths as possible, subject to resource constraints for meeting the needs of youth. Currently, the assignment is manually done by humans working in the housing communities. In this paper, we consider the problem of assigning homeless youth to housing programs subject to resource constraints. We provide an initial abstract model for this setting and show that the problem of maximizing the total assigned youth to the programs under this model is APX-hard. To solve the problem, we non-trivially formulate it as a multiple multi-dimensional knapsack problem (MMDKP), which is not known to have any approximation algorithm. We provide a first interpretable and easy-to-use greedy algorithm with logarithmic approximation ratio for solving general MMDKP. We conduct experiments on random and realistic instances of the housing assignment settings and show that our algorithm is efficient and effective in solving large instances (up to 1 million youth).

More than 1 million homicides, robberies, and aggravated assaults occur in the United States each year. These crimes are often further classified into different types based on the circumstances surrounding the crime (e.g., domestic violence, gang-related). Despite recent technological advances in AI and machine learning, these additional classification tasks are still done manually by specially trained police officers. In this paper, we provide the first attempt to develop a more automatic system for classifying crimes. In particular, we study the question of classifying whether a given violent crime is gang-related. We introduce a novel Partially Generative Neural Networks (PGNN) that is able to accurately classify gang-related crimes both when full information is available and when there is only partial information. Our PGNN is the first generative-classification model that enables to work when some features of the test examples are missing. Using a crime event dataset from Los Angeles covering 2014-2016, we experimentally show that our PGNN outperforms all other typically used classifiers for the problem of classifying gang-related violent crimes.

We consider the problem of computing a mixed-strategy Nash equilibrium (MSNE) in resource graph games (RGGs), a compact representation for games with an exponential number of strategies. In an RGG, each player's pure strategy is a subset of resources, represented by a binary vector, and her pure strategy set is represented compactly using a set of linear inequality constraints. Given the pure strategies of the players, each player's utility depends on the resource graph and the numbers of times the neighboring resources are used. RGGs are general enough to capture a wide variety of games studied in literature, including congestion games and security games.In this paper, we provide the first Fully Polytnomial Time Approximation Scheme (FPTAS) for computing an MSNE in any symmetric multilinear RGG where its constraint moralized resource graph (a graph formed between the moralized resource graph and the constraints defining the strategy polytope) has bounded treewidth. Our FPTAS can be generalized to compute optimal MSNE, and to games with a constant number of player types. As a consequence, our FPTAS provides new approximation results for security games, network congestion games, and bilinear games.

In many real-world systems, strategic agents' decisions can be understood as complex - i.e., consisting of multiple sub-decisions - and hence can give rise to an exponential number of pure strategies. Examples include network congestion games, simultaneous auctions, and security games. However, agents' sets of strategies are often structured, allowing them to be represented compactly. There currently exists no general modeling language that captures a wide range of commonly seen strategy structure and utility structure. We propose Resource Graph Games (RGGs), the first general compact representation for games with structured strategy spaces, which is able to represent a wide range of games studied in literature. We leverage recent results about multilinearity, a key property of games that allows us to represent the mixed strategies compactly, and, as a result, to compute various equilibrium concepts efficiently. While not all RGGs are multilinear, we provide a general method of converting RGGs to those that are multilinear, and identify subclasses of RGGs whose converted version allow efficient computation.

This paper presents HEALER, a software agent that recommends sequential intervention plans for use by homeless shelters, who organize these interventions to raise awareness about HIV among homeless youth. HEALER's sequential plans (built using knowledge of social networks of homeless youth) choose intervention participants strategically to maximize influence spread, while reasoning about uncertainties in the network. While previous work presents influence maximizing techniques to choose intervention participants, they do not address two real-world issues: (i) they completely fail to scale up to real-world sizes; and (ii) they do not handle deviations in execution of intervention plans. HEALER handles these issues via two major contributions: (i) HEALER casts this influence maximization problem as a POMDP and solves it using a novel planner which scales up to previously unsolvable real-world sizes; and (ii) HEALER allows shelter officials to modify its recommendations, and updates its future plans in a deviation-tolerant manner. HEALER was deployed in the real world in Spring 2016 with considerable success.

Roughly speaking, Interdependent Defense (IDD) games, previously proposed, model the situation where an attacker wants to cause as much damage as possible to a network by attacking one of the sites in the network. Each site must make an investment decision regarding security to protect itself against a direct or indirect attack, the latter due to potential transfer-risk from an unprotected neighboring site. The work introducing IDD games discusses potential applications to model the essence of real-world scenarios such as the 2006 transatlantic aircraft plot. In this paper, our focus is the study of the problem of computing a Nash Equilibrium (NE) in IDD games. We show that an efficient algorithm to determine whether some attacker’s strategy can be a part of a NE in an instance of IDD games is unlikely to exist. Yet, we provide a dynamic programming algorithm to compute an approximate NE when the graph/network structure of the game is a directed tree with a single source, and show that it is an FPTAS. We also introduce an improved heuristic to compute an approximate NE on arbitrary graph structures. Our experiments show that our heuristic is more efficient, and provides better approximations, than best-response-gradient dynamics for the case of Internet games, a class of games introduced and studied in the original work on IDD games.

Robustness is a critical measure of the resilience of large networked systems, such as transportation and communication networks. Most prior works focus on the global robustness of a given graph at large, e.g., by measuring its overall vulnerability to external attacks or random failures. In this paper, we turn attention to local robustness and pose a novel problem in the lines of subgraph mining: given a large graph, how can we find its most robust local subgraph (RLS)? We define a robust subgraph as a subset of nodes with high communicability [15] among them, and formulate the RLS-PROBLEM of finding a subgraph of given size with maximum robustness in the host graph. Our formulation is related to the recently proposed general framework [39] for the densest subgraph problem, however differs from it substantially in that besides the number of edges in the subgraph, robustness also concerns with the placement of edges, i.e., the subgraph topology. We show that the RLS-PROBLEM is NP-hard and propose two heuristic algorithms based on top-down and bottom-up search strategies. Further, we present modifications of our algorithms to handle three practical variants of the RLS-PROBLEM. Experiments on synthetic and real-world graphs demonstrate that we find subgraphs with larger robustness than the densest subgraphs [9, 39] even at lower densities, suggesting that the existing approaches are not suitable for the new problem setting.

The function and performance of networks rely on their robustness, defined as their ability to continue functioning in the face of damage (targeted attacks or random failures) to parts of the network. Prior research has proposed a variety of measures to quantify robustness and various manipulation strategies to alter it. In this paper, our contributions are twofold. First, we critically analyze various robustness measures and identify their strengths and weaknesses. Our analysis suggests natural connectivity, based on the weighted count of loops in a network, to be a reliable measure. Second, we propose the first principled manipulation algorithms that directly optimize this robustness measure, which lead to significant performance improvement over existing, ad-hoc heuristic solutions. Extensive experiments on real-world datasets demonstrate the effectiveness and scalability of our methods against a long list of competitor strategies.

Given a topic and its top-k most relevant words generated by a topic model, how can we tell whether it is a low-quality or a high-quality topic? Topic models provide a low-dimensional representation of large document corpora, and drive many important applications such as summarization, document segmentation, word-sense disambiguation, etc. Evaluation of topic models is an important issue, since low-quality topics potentially degrade the performance of these applications. In this paper, we develop a graph mining and machine learning approach for the external evaluation of topic models. Based on the graph-centric features we extract from the projection of topic words on the Wikipedia page-links graph, we learn models that can predict the human-perceived quality of topics (based on human judgments), and classify them as high or low quality. Experiments on four real-world corpora show that our approach boosts the prediction performance up to 30% over three baselines of various complexities, and demonstrate the generality of our method to diverse domains. In addition, we provide an interpretation of our models and outline the discriminating characteristics of topic quality.