The problem of distributed learning and channel access is considered in a cognitive network with multiple secondary users. The availability statistics of the channels are initially unknown to the secondary users and are estimated using sensing decisions. There is no explicit information exchange or prior agreement among the secondary users. We propose policies for distributed learning and access which achieve order-optimal cognitive system throughput (number of successful secondary transmissions) under self play, i.e., when implemented at all the secondary users. Equivalently, our policies minimize the regret in distributed learning and access. We first consider the scenario when the number of secondary users is known to the policy, and prove that the total regret is logarithmic in the number of transmission slots. Our distributed learning and access policy achieves order-optimal regret by comparing to an asymptotic lower bound for regret under any uniformly-good learning and access policy. We then consider the case when the number of secondary users is fixed but unknown, and is estimated through feedback. We propose a policy in this scenario whose asymptotic sum regret which grows slightly faster than logarithmic in the number of transmission slots.Index Terms-Cognitive medium access control, multi-armed bandits, distributed algorithms, logarithmic regret. † Corresponding author.A. Anandkumar is with the

The problem of cooperative allocation among multiple secondary users to maximize cognitive system throughput is considered. The channel availability statistics are initially unknown to the secondary users and are learnt via sensing samples. Two distributed learning and allocation schemes which maximize the cognitive system throughput or equivalently minimize the total regret in distributed learning and allocation are proposed. The first scheme assumes minimal prior information in terms of pre-allocated ranks for secondary users while the second scheme is fully distributed and assumes no such prior information. The two schemes have sum regret which is provably logarithmic in the number of sensing time slots. A lower bound is derived for any learning scheme which is asymptotically logarithmic in the number of slots. Hence, our schemes achieve asymptotic order optimality in terms of regret in distributed learning and allocation.

Abstract-We present HALO, the first link-state routing solution with hop-by-hop packet forwarding that minimizes the cost of carrying traffic through packet-switched networks. At each node , for every other node , the algorithm independently and iteratively updates the fraction of traffic destined to that leaves on each of its outgoing links. At each iteration, the updates are calculated based on the shortest path to each destination as determined by the marginal costs of the network's links. The marginal link costs used to find the shortest paths are in turn obtained from link-state updates that are flooded through the network after each iteration. For stationary input traffic, we prove that HALO converges to the routing assignment that minimizes the cost of the network. Furthermore, we observe that our technique is adaptive, automatically converging to the new optimal routing assignment for quasi-static network changes. We also report numerical and experimental evaluations to confirm our theoretical predictions, explore additional aspects of the solution, and outline a proof-of-concept implementation of HALO.Index Terms-IP networks, load balancing, network management, optimal routing.

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Abstract-The problem of distributed learning and channel access is considered in a cognitive network with multiple secondary users. The availability statistics of the channels are initially unknown to the secondary users and are estimated using sensing decisions. There is no explicit information exchange or prior agreement among the secondary users. We propose policies for distributed learning and access which achieve order-optimal cognitive system throughput (number of successful secondary transmissions) under self play, i.e., when implemented at all the secondary users. Equivalently, our policies minimize the regret in distributed learning and access. We first consider the scenario when the number of secondary users is known to the policy, and prove that the total regret is logarithmic in the number of transmission slots. Our distributed learning and access policy achieves order-optimal regret by comparing to an asymptotic lower bound for regret under any uniformly-good learning and access policy. We then consider the case when the number of secondary users is fixed but unknown, and is estimated through feedback. We propose a policy in this scenario whose asymptotic sum regret which grows slightly faster than logarithmic in the number of transmission slots.Index Terms-Cognitive medium access control, multi-armed bandits, distributed algorithms, logarithmic regret.