Adaptive Regret Minimization in Bounded-Memory Games

Online learning algorithms that minimize regret provide strong guarantees in situations that involve repeatedly making decisions in an uncertain environment, e.g. a driver deciding what route to drive to work every day. While regret minimization has been extensively studied in repeated games, we study regret minimization for a richer class of games called bounded memory games. In each round of a two-player bounded memory-m game, both players simultaneously play an action, observe an outcome and receive a reward. The reward may depend on the last m outcomes as well as the actions of the players in the current round. The standard notion of regret for repeated games is no longer suitable because actions and rewards can depend on the history of play. To account for this generality, we introduce the notion of k-adaptive regret, which compares the reward obtained by playing actions prescribed by the algorithm against a hypothetical k-adaptive adversary with the reward obtained by the best expert in hindsight against the same adversary. Roughly, a hypothetical k-adaptive adversary adapts her strategy to the defender's actions exactly as the real adversary would within each window of k rounds. Our definition is parametrized by a set of experts, which can include both fixed and adaptive defender strategies. We investigate the inherent complexity of and design algorithms for adaptive regret minimization in bounded memory games of perfect and imperfect information. We prove a hardness result showing that, with imperfect information, any k-adaptive regret minimizing algorithm (with fixed strategies as experts) must be inefficient unless NP=RP even when playing against an oblivious adversary. In contrast, for bounded memory games of perfect and imperfect information we present approximate 0-adaptive regret minimization algorithms against an oblivious adversary running in time n^{O(1)}.Comment: Full Version. GameSec 2013 (Invited Paper

Time lower bounds for nonadaptive turnstile streaming algorithms

We say a turnstile streaming algorithm is "non-adaptive" if, during updates, the memory cells written and read depend only on the index being updated and random coins tossed at the beginning of the stream (and not on the memory contents of the algorithm). Memory cells read during queries may be decided upon adaptively. All known turnstile streaming algorithms in the literature are non-adaptive. We prove the first non-trivial update time lower bounds for both randomized and deterministic turnstile streaming algorithms, which hold when the algorithms are non-adaptive. While there has been abundant success in proving space lower bounds, there have been no non-trivial update time lower bounds in the turnstile model. Our lower bounds hold against classically studied problems such as heavy hitters, point query, entropy estimation, and moment estimation. In some cases of deterministic algorithms, our lower bounds nearly match known upper bounds

How a well-adapting immune system remembers

An adaptive agent predicting the future state of an environment must weigh trust in new observations against prior experiences. In this light, we propose a view of the adaptive immune system as a dynamic Bayesian machinery that updates its memory repertoire by balancing evidence from new pathogen encounters against past experience of infection to predict and prepare for future threats. This framework links the observed initial rapid increase of the memory pool early in life followed by a mid-life plateau to the ease of learning salient features of sparse environments. We also derive a modulated memory pool update rule in agreement with current vaccine response experiments. Our results suggest that pathogenic environments are sparse and that memory repertoires significantly decrease infection costs even with moderate sampling. The predicted optimal update scheme maps onto commonly considered competitive dynamics for antigen receptors

Development and function of protective and pathologic memory CD4 T cells

Immunological memory is one of the defining features of the adaptive immune system. As key orchestrators and mediators of immunity, CD4 T cells are central to the vast majority of adaptive immune responses. Generated following an immune response, memory CD4 T cells retain pertinent information about their activation environment enabling them to make rapid effector responses upon reactivation. These responses can either benefit the host by hastening the control of pathogens or cause damaging immunopathology. Here, we will discuss the diversity of the memory CD4 T cell pool, the signals that influence the transition of activated T cells into that pool, and highlight how activation requirements differ between naïve and memory CD4 T cells. A greater understanding of these factors has the potential to aid the design of more effective vaccines and to improve regulation of pathologic CD4 T cells, such as in the context of autoimmunity and allergy

Enhanced winnings in a mixed-ability population playing a minority game

We study a mixed population of adaptive agents with small and large memories, competing in a minority game. If the agents are sufficiently adaptive, we find that the average winnings per agent can exceed that obtainable in the corresponding pure populations. In contrast to the pure population, the average success rate of the large-memory agents can be greater than 50 percent. The present results are not reproduced if the agents are fed a random history, thereby demonstrating the importance of memory in this system.Comment: 9 pages Latex + 2 figure

HAPPY: Hybrid Address-based Page Policy in DRAMs

Memory controllers have used static page closure policies to decide whether a row should be left open, open-page policy, or closed immediately, close-page policy, after the row has been accessed. The appropriate choice for a particular access can reduce the average memory latency. However, since application access patterns change at run time, static page policies cannot guarantee to deliver optimum execution time. Hybrid page policies have been investigated as a means of covering these dynamic scenarios and are now implemented in state-of-the-art processors. Hybrid page policies switch between open-page and close-page policies while the application is running, by monitoring the access pattern of row hits/conflicts and predicting future behavior. Unfortunately, as the size of DRAM memory increases, fine-grain tracking and analysis of memory access patterns does not remain practical. We propose a compact memory address-based encoding technique which can improve or maintain the performance of DRAMs page closure predictors while reducing the hardware overhead in comparison with state-of-the-art techniques. As a case study, we integrate our technique, HAPPY, with a state-of-the-art monitor, the Intel-adaptive open-page policy predictor employed by the Intel Xeon X5650, and a traditional Hybrid page policy. We evaluate them across 70 memory intensive workload mixes consisting of single-thread and multi-thread applications. The experimental results show that using the HAPPY encoding applied to the Intel-adaptive page closure policy can reduce the hardware overhead by 5X for the evaluated 64 GB memory (up to 40X for a 512 GB memory) while maintaining the prediction accuracy

The size of the immune repertoire of bacteria

Some bacteria and archaea possess an immune system, based on the CRISPR-Cas mechanism, that confers adaptive immunity against phage. In such species, individual bacteria maintain a "cassette" of viral DNA elements called spacers as a memory of past infections. The typical cassette contains a few dozen spacers. Given that bacteria can have very large genomes, and since having more spacers should confer a better memory, it is puzzling that so little genetic space would be devoted by bacteria to their adaptive immune system. Here, we identify a fundamental trade-off between the size of the bacterial immune repertoire and effectiveness of response to a given threat, and show how this tradeoff imposes a limit on the optimal size of the CRISPR cassette.Comment: 9 pages, 5 figure