Motivated by the widespread adoption of large-scale A/B testing in industry, we propose a new experimentation framework for the setting where potential experiments are abundant (i.e., many hypotheses are available to test), and observations are costly; we refer to this as the experiment-rich regime. Such scenarios require the experimenter to internalize the opportunity cost of assigning a sample to a particular experiment. We fully characterize the optimal policy and give an algorithm to compute it. Furthermore, we develop a simple heuristic that also provides intuition for the optimal policy. We use simulations based on real data to compare both the optimal algorithm and the heuristic to other natural alternative experimental design frameworks. In particular, we discuss the paradox of power: high-powered "classical" tests can lead to highly inefficient sampling in the experiment-rich regime.

Motivated by the application of real-time pricing in e-commerce platforms, we consider the problem of revenue-maximization in a setting where the seller can leverage contextual information describing the customer's history and the product's type to predict her valuation of the product. However, her true valuation is unobservable to the seller, only binary outcome in the form of success-failure of a transaction is observed. Unlike in usual contextual bandit settings, the optimal price/arm given a covariate in our setting is sensitive to the detailed characteristics of the residual uncertainty distribution. We develop a semi-parametric model in which the residual distribution is non-parametric and provide the first algorithm which learns both regression parameters and residual distribution with $\tilde O(\sqrt{n})$ regret. We empirically test a scalable implementation of our algorithm and observe good performance.

In many platforms, user arrivals exhibit a self-reinforcing behavior: future user arrivals are likely to have preferences similar to users who were satisfied in the past. In other words, arrivals exhibit {\em positive externalities}. We study multiarmed bandit (MAB) problems with positive externalities. We show that the self-reinforcing preferences may lead standard benchmark algorithms such as UCB to exhibit linear regret. We develop a new algorithm, Balanced Exploration (BE), which explores arms carefully to avoid suboptimal convergence of arrivals before sufficient evidence is gathered. We also introduce an adaptive variant of BE which successively eliminates suboptimal arms. We analyze their asymptotic regret, and establish optimality by showing that no algorithm can perform better.

Finding a document or resource in an unstructured peer-to-peer network can be an exceedingly difficult problem. In this paper we propose a query routing approach that accounts for arbitrary overlay topologies, nodes with heterogeneous processing capacity, e.g., reflecting their degree of altruism, and heterogenous class-based likelihoods of query resolution at nodes which may reflect query loads and the manner in which files/resources are distributed across the network. The approach is shown to be stabilize the query load subject to a grade of service constraint, i.e., a guarantee that queries' routes meet pre-specified class-based bounds on their associated a priori probability of query resolution. An explicit characterization of the capacity region for such systems is given and numerically compared to that associated with random walk based searches. Simulation results further show the performance benefits, in terms of mean delay, of the proposed approach. Additional aspects associated with reducing complexity, estimating parameters, and adaptation to class-based query resolution probabilities and traffic loads are studied.

We consider multi-class queueing systems where the per class service rates depend on the network state, fairness criterion, and is constrained to be in a symmetric polymatroid capacity region. We develop new comparison results leading to explicit bounds on the mean service time under various fairness criteria and possibly heterogeneous loads. We then study large-scale systems with growing numbers of service classes n (e.g., files), heterogenous servers m and polymatroid capacity resulting from a random bipartite graph modeling service availability (e.g., placement of files across servers). This models, for example, a large scale content delivery network (CDN) supporting parallel servicing of a download request. For an appropriate asymptotic regime, we show that the system's capacity region is uniformly close to a symmetric polymatroid -- i.e., heterogeneity in servers' capacity and file placement disappears.

We consider a centralized content delivery infrastructure where a large number of storage-intensive files are replicated across several collocated servers. To achieve scalable mean delays in file downloads under stochastic loads, we allow multiple servers to work together as a pooled resource to meet individual download requests. In such systems, basic questions include: How and where to replicate files? What is the impact of dynamic service allocation across request types, and whether such allocations can provide substantial gains over simpler load balancing policies? What are tradeoffs among performance, reliability and recovery costs, and energy? This paper provides a simple performance model for large systems towards addressing these basic questions.

Large scale Content Delivery Networks (CDNs) are one of the key components of today's information infrastructure. This paper proposes and analyzes a simple stochastic model for a file-server system wherein servers can work together, as a pooled resource, to meet individual user requests. In such systems basic questions include: How and where to replicate files? What is the impact of dynamic service allocation across request types, and whether it can provide substantial gains over simpler load balancing policies? What are tradeoffs amongst performance, reliability and recovery costs, and energy? The paper provides both explicit and asymptotic approximations for large systems towards addressing these basic questions.

We consider in-network computation of an arbitrary function over an arbitrary communication network. A network with capacity constraints on the links is given. Some nodes in the network generate data, e.g., like sensor nodes in a sensor network. An arbitrary function of this distributed data is to be obtained at a terminal node. The structure of the function is described by a given computation schema, which in turn is represented by a directed tree. We design computing and communicating schemes to obtain the function at the terminal at the maximum rate. For this, we formulate linear programs to determine network flows that maximize the computation rate. We then develop a fast combinatorial primal-dual algorithm to obtain near-optimal solutions to these linear programs. As a subroutine for this, we develop an algorithm for finding the minimum cost embedding of a tree in a network with any given set of link costs. We then briefly describe extensions of our techniques to the cases of multiple terminals wanting different functions, multiple computation schemas for a function, computation with a given desired precision, and to networks with energy constraints at nodes.

Finding a document or resource in an unstructured peer-to-peer network can be an exceedingly difficult problem. In this paper we propose a dynamic query routing approach that accounts for arbitrary overlay topologies, nodes with heterogeneous processing capacity and heterogenous class-based likelihoods of query resolution at nodes, reflecting the query loads and manner in which files/resources are distributed across the network. Finite processing capacity at nodes, e.g., reflecting their degree of altruism, can indeed limit the stabilizable load into the system. Our approach is shown to be throughput optimal subject to a grade of service constraint, i.e., it stabilizes the query load subject to a guarantee that queries' routes meet pre-specified class-based bounds on their associated a priori probability of query resolution. Numerical and simulation results show significant improvement in capacity region and performance benefits, in terms of mean delay, over random walk based searches. Additional aspects associated with reducing complexity, learning, and adaptation to class-based query resolution probabilities and traffic loads are studied.

We consider in-network computation of an arbitrary function over an arbitrary communication network. We consider the same model as our earlier work in [1]. The given network consists of directed/undirected links with capacity constraints, some source nodes which generate data, and other intermediate forwarding nodes. An arbitrary function of this distributed data is to be computed at a terminal node. The structure of the function is described by a given computation schema represented by a directed tree. In our earlier work, we presented a linear program to define the maximum rate of computation, and then introduced a notion of flow-conservation suitable in this context so as to come up with a flow-conservation based linear program which can be solved in polynomial time. In this paper, we develop a combinatorial primal-dual algorithm to obtain (1-∈)-approximate solutions to these linear programs. As a part of this, we present an algorithm to find a minimum-cost embedding in a network of weighted links--which is of independent interest. We then describe application of our techniques to other practically interesting problems of multiple terminals wanting different functions, computation with a given desired precision, and to networks with energy constraints at nodes.

We consider in-network computation of an arbitrary function over an arbitrary communication network. A network with capacity constraints on the links is given. Some nodes in the network generate data, e.g., sensor nodes in a sensor network. An arbitrary function of this distributed data is to be obtained at a terminal node. The structure of the function is described by a given computation schema, which in turn is represented by a directed tree. We define a new notion of conservation of flow suitable in this setup and design computing and communicating schemes to obtain the function at the terminal at the maximum rate. For this, we formulate linear programs to determine network flows that maximize the computation rate. Our approach introduces the network flow techniques to the distributed function computation setup where such a scope was hitherto unsuspected due to the lack of traditional conservation of flow.

Cooperative wireless systems can exploit spatial diversity by opportunistically selecting the best relay to forward data to a destination. However, determining the best relay is a challenging task and requires a selection algorithm because the relays are geographically separated and only have local channel knowledge. Selecting the best relay is equivalent to finding the relay with the largest metric, where each relay computes its metric using local channel knowledge. We analyze the performance of a fast, distributed, and scalable multiple access based selection algorithm when it assumes incorrect values for two fundamental parameters that it requires to operate efficiently - the number of available relays and the cumulative distribution function (CDF) of the metrics. Such imperfect knowledge will invariably arise in practice. We develop new expressions for the time required to select the best relay as a function of the assumed and actual parameters. We show that imperfect knowledge can significantly slow down the selection algorithm. Further, in a system that uses its observations to update its CDF estimate, we determine the minimum number of observations required to limit the performance degradation. We also develop a minimax formulation that makes the algorithm robust to uncertainties in the number of relays in the system.

Timer-based mechanisms are often used in several wireless systems to help a given (sink) node select the best helper node among many available nodes. Specifically, a node transmits a packet when its timer expires, and the timer value is a function of its local suitability metric. In practice, the best node gets selected successfully only if no other node's timer expires within a `vulnerability' window after its timer expiry. In this paper, we provide a complete closed-form characterization of the optimal metric-to-timer mapping that maximizes the probability of success for any probability distribution function of the metric. The optimal scheme is scalable, distributed, and much better than the popular inverse metric timer mapping. We also develop an asymptotic characterization of the optimal scheme that is elegant and insightful, and accurate even for a small number of nodes.

Timer-based mechanisms are often used to help a given (sink) node select the best helper node from among many available nodes. In these, a node transmits a packet when its timer expires. The timer value is a monotone non-increasing function of its local suitability metric, which ensures that the best node is the first to transmit and is selected successfully if no other node's timer expires within a 'vulnerability' window after its timer expiry and so long as the sink can hear the available nodes. In this paper, we show that the optimal metric-to-timer mapping that (i) maximizes the probability of successful selection or (ii) minimizes the average selection time subject to a minimum constraint on the probability of success, maps the metric into a set of discrete timer values. We specify, in closed-form, the optimal scheme as a function of the maximum selection duration, the vulnerability window, and the number of nodes. An asymptotic characterization of the optimal scheme turns out to be elegant and insightful. For any probability distribution function of the metric, the optimal scheme is scalable, distributed, and performs much better than the popular inverse metric timer mapping. It even compares favorably with splitting-based selection, when the latter's feedback overhead is accounted for.

Relay selection for cooperative communications promises significant performance improvements, and is, therefore, attracting considerable attention. While several criteria have been proposed for selecting one or more relays, distributed mechanisms that perform the selection have received relatively less attention. In this paper, we develop a novel, yet simple, asymptotic analysis of a splitting-based multiple access selection algorithm to find the single best relay. The analysis leads to simpler and alternate expressions for the average number of slots required to find the best user. By introducing a new `contention load¿ parameter, the analysis shows that the parameter settings used in the existing literature can be improved upon. New and simple bounds are also derived. Furthermore, we propose a new algorithm that addresses the general problem of selecting the best Q ¿ 1 relays, and analyze and optimize it. Even for a large number of relays, the scalable algorithm selects the best two relays within 4.406 slots and the best three within 6.491 slots, on average. We also propose a new and simple scheme for the practically relevant case of discrete metrics. Altogether, our results develop a unifying perspective about the general problem of distributed selection in cooperative systems and several other multi-node systems.

A common and practical paradigm in cooperative communication systems is the use of a dynamically selected "best" relay to decode and forward information from a source to a destination. Such systems use two phases - a relay selection phase, in which the system uses transmission time and energy to select the best relay, and a data transmission phase, in which it uses the spatial diversity benefits of selection to transmit data. In this paper, we derive closed-form expressions for the overall throughput and energy consumption, and study the time and energy trade-off between the selection and data transmission phases. To this end, we analyze a baseline non-adaptive system and several adaptive systems that adapt the selection phase, relay transmission power, or transmission time. Our results show that while selection yields significant benefits, the selection phase's time and energy overhead can be significant. In fact, at the optimal point, the selection can be far from perfect, and depends on the number of relays and the mode of adaptation. The results also provide guidelines about the optimal system operating point for different modes of adaptation. The analysis also sheds new insights on the fast splitting-based algorithm considered in this paper for relay selection.

A common and practical paradigm in cooperative communications is the use of a dynamically selected 'best' relay to decode and forward information from a source to a destination. Such a system consists of two core phases: a relay selection phase, in which the system expends resources to select the best relay, and a data transmission phase, in which it uses the selected relay to forward data to the destination. In this paper, we study and optimize the trade-off between the selection and data transmission phase durations. We derive closed-form expressions for the overall throughput of a non-adaptive system that includes the selection phase overhead, and then optimize the selection and data transmission phase durations. Corresponding results are also derived for an adaptive system in which the relays can vary their transmission rates. Our results show that the optimal selection phase overhead can be significant even for fast selection algorithms. Furthermore, the optimal selection phase duration depends on the number of relays and whether adaptation is used.

Relay selection for cooperative communications has attracted considerable research interest recently. While several criteria have been proposed for selecting one or more relays and analyzed, mechanisms that perform the selection in a distributed manner have received relatively less attention. In this paper, we analyze a splitting algorithm for selecting the single best relay amongst a known number of active nodes in a cooperative network. We develop new and exact asymptotic analysis for computing the average number of slots required to resolve the best relay. We then propose and analyze a new algorithm that addresses the general problem of selecting the best Q ges 1 relays. Regardless of the number of relays, the algorithm selects the best two relays within 4.406 slots and the best three within 6.491 slots, on average. Our analysis also brings out an intimate relationship between multiple access selection and multiple access control algorithms.