Swaprava Nath

Theory and algorithms for hop-count-based localization with random geometric graph models of dense sensor networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes in a region of Euclidean space. Following deployment, the nodes self-organize into a mesh topology with a key aspect being self-localization. Having obtained a mesh topology in a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this work, we analyze this approximation through two complementary analyses. We assume that the mesh topology is a random geometric graph on the nodes; and that some nodes are designated as anchors with known locations. First, we obtain high probability bounds on the Euclidean distances of all nodes that are h hops away from a fixed anchor node. In the second analysis, we provide a heuristic argument that leads to a direct approximation for the density function of the Euclidean distance between two nodes that are separated by a hop distance h. This approximation is shown, through simulation, to very closely match the true density function. Localization algorithms that draw upon the preceding analyses are then proposed and shown to perform better than some of the well-known algorithms present in the literature. Belief-propagation-based message-passing is then used to further enhance the performance of the proposed localization algorithms. To our knowledge, this is the first usage of message-passing for hop-count-based self-localization.

Game-Theoretic Modeling of Human Adaptation in Human-Robot Collaboration

In human-robot teams, humans often start with an inaccurate model of the robot capabilities. As they interact with the robot, they infer the robots capabilities and partially adapt to the robot, i.e., they might change their actions based on the observed outcomes and the robots actions, without replicating the robots policy. We present a game-theoretic model of human partial adaptation to the robot, where the human responds to the robots actions by maximizing a reward function that changes stochastically over time, capturing the evolution of their expectations of the robots capabilities. The robot can then use this model to decide optimally between taking actions that reveal its capabilities to the human and taking the best action given the information that the human currently has. We prove that under certain observability assumptions, the optimal policy can be computed efficiently. We demonstrate through a human subject experiment that the proposed model significantly improves human-robot team performance, compared to policies that assume complete adaptation of the human to the robot.

Mechanism design for time critical and cost critical task execution via crowdsourcing

An exciting application of crowdsourcing is to use social networks in complex task execution. In this paper, we address the problem of a planner who needs to incentivize agents within a network in order to seek their help in executing an atomic task as well as in recruiting other agents to execute the task. We study this mechanism design problem under two natural resource optimization settings: (1) cost critical tasks, where the planners goal is to minimize the total cost, and (2) time critical tasks, where the goal is to minimize the total time elapsed before the task is executed. We identify a set of desirable properties that should ideally be satisfied by a crowdsourcing mechanism. In particular, sybil-proofness and collapse-proofness are two complementary properties in our desiderata. We prove that no mechanism can satisfy all the desirable properties simultaneously. This leads us naturally to explore approximate versions of the critical properties. We focus our attention on approximate sybil-proofness and our exploration leads to a parametrized family of payment mechanisms which satisfy collapse-proofness. We characterize the approximate versions of the desirable properties in cost critical and time critical domain.

Subset Selection Via Implicit Utilitarian Voting

How should one aggregate ordinal preferences expressed by voters into a measurably superior social choice? A well-established approach -- which we refer to as implicit utilitarian voting -- assumes that voters have latent utility functions that induce the reported rankings, and seeks voting rules that approximately maximize utilitarian social welfare. We extend this approach to the design of rules that select a subset of alternatives. We derive analytical bounds on the performance of optimal (deterministic as well as randomized) rules in terms of two measures, distortion and regret. Empirical results show that regret-based rules are more compelling than distortion-based rules, leading us to focus on developing a scalable implementation for the optimal (deterministic) regret-based rule. Our methods underlie the design and implementation of an upcoming social choice website.

Performance evaluation of distance-hop proportionality on geometric graph models of dense sensor networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes on a region in Euclidean space, e.g., the unit square. After deployment, the nodes self-organise into a mesh topology. In a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this paper, we analyse the performance of this approximation. We show that nodes with a certain hop distance from a fixed anchor node lie within a certain annulus with probability approaching unity as the number of nodes n → ∞. We take a uniform, i.i.d. deployment of n nodes on a unit square, and consider the geometric graph on these nodes with radius r(n) = c√1n n/n. We show that, for a given hop distance h of a node from a fixed anchor on the unit square, the Euclidean distance lies within [(1-e)(h-1)r(n), hr(n)], for e > 0, with probability approaching unity as n → ∞. This result shows that it is more likely to expect a node, with hop distance h from the anchor, to lie within this annulus centred at the anchor location, and of width roughly r(n), which decreases as n increases. We show that if the radius r of the geometric graph is fixed, the convergence of the probability is exponentially fast. Similar results hold for a randomised lattice deployment. We provide simulation results that illustrate the theory, and serve to show how large n needs to be for the asymptotics to be useful.

Affine Maximizers in Domains with Selfish Valuations

We consider the domain of selfish and continuous preferences over a “rich” allocation space and show that onto, strategyproof and allocation non-bossy social choice functions are affine maximizers. Roberts [1979] proves this result for a finite set of alternatives and an unrestricted valuation space. In this article, we show that in a subdomain of the unrestricted valuations with the additional assumption of allocation non-bossiness, using the richness of the allocations, the strategyproof social choice functions can be shown to be affine maximizers. We provide an example to show that allocation non-bossiness is indeed critical for this result. This work shows that an affine maximizer result needs a certain amount of richness split across valuations and allocations.

Separability and decomposition in mechanism design with transfers

Abstract In private values quasi-linear environment, we consider problems where allocation decisions along multiple components have to be made. Every agent has additively separable valuation over the components. We show that every unanimous and dominant strategy implementable allocation rule in this problem is a component-wise weighted utilitarian rule, which assigns non-negative weight vectors to agents in each component and chooses an alternative in each component by maximizing the weighted sum of valuations in that component. A corollary of our result is that every unanimous and dominant strategy implementable allocation rule can be almost decomposed (modulo tie-breaking) into dominant strategy implementable allocation rules along each component.

Efficiency and Budget Balance

We study efficiency and budget balance for designing mechanisms in general quasi-linear domains. Green and Laffonti¾?[13] proved that one cannot generically achieve both. We consider strategyproof budget-balanced mechanisms that are approximately efficient. For deterministic mechanisms, we show that a strategyproof and budget-balanced mechanism must have a sink agent whose valuation function is ignored in selecting an alternative, and she is compensated with the payments made by the other agents. We assume the valuations of the agents come from a bounded open interval. This result strengthens Green and Laffonts impossibility result by showing that even in a restricted domain of valuations, there does not exist a mechanism that is strategyproof, budget balanced, and takes every agents valuation into consideration--a corollary of which is that it cannot be efficient. Using this result, we find a tight lower bound on the inefficiencies of strategyproof, budget-balanced mechanisms in this domain. The bound shows that the inefficiency asymptotically disappears when the number of agents is large--a result close in spirit to Green and Laffonti¾?[13, Theorem 9.4]. However, our results provide worst-case bounds and the best possible rate of convergence. Next, we consider minimizing any convex combination of inefficiency and budget imbalance. We show that if the valuations are unrestricted, no deterministic mechanism can do asymptotically better than minimizing inefficiency alone. Finally, we investigate randomized mechanisms and provide improved lower bounds on expected inefficiency. We give a tight lower bound for an interesting class of strategyproof, budget-balanced, randomized mechanisms. We also use an optimization-based approach--in the spirit of automated mechanism design--to provide a lower bound on the minimum achievable inefficiency of any randomized mechanism. Experiments with real data from two applications show that the inefficiency for a simple randomized mechanism is 5---100 times smaller than the worst case. This relative difference increases with the number ofi¾?agents.

Dynamic learning-based mechanism design for dependent valued exchange economies

Learning private information from multiple strategic agents poses challenge in many Internet applications. Sponsored search auctions, crowdsourcing, Amazons mechanical turk, various online review forums are examples where we are interested in learning true values of the advertisers or true opinion of the reviewers. The common thread in these decision problems is that the optimal outcome depends on the private information of all the agents, while the decision of the outcome can be chosen only through reported information which may be manipulated by the strategic agents. The other important trait of these applications is their dynamic nature. The advertisers in an online auction or the users of mechanical turk arrive and depart, and when present, interact with the system repeatedly, giving the opportunity to learn their types. Dynamic mechanisms, which learn from the past interactions and make present decisions depending on the expected future evolution of the game, has been shown to improve performance over repeated versions of static mechanisms. In this paper, we will survey the past and current state-of-the-art dynamic mechanisms and analyze a new setting where the agents consist of buyers and sellers, known as exchange economies, and agents having value interdependency, which are relevant in applications illustrated through examples. We show that known results of dynamic mechanisms with independent value settings cannot guarantee certain desirable properties in this new significantly different setting. In the future work, we propose to analyze similar settings with dynamic types and population.