| The success of autonomic computing will hinge on the extent to which theorists can identify universal principles that span the multiple levels at which autonomic systems can exist—from systems to enterprises to economies. Behavioral Abstractions and Models Defining appropriate abstractions and models for understanding, controlling, and designing emergent behavior in autonomic systems is the challenge at the heart of autonomic computing. We need fundamental mathematical work aimed at understanding how the properties of self-configuration, self-optimization, self-maintenance, and robustness arise from or depend on the behaviors, goals, and adaptivity of individual autonomic elements; the pattern and type of interactions among them; and the external influences or demands on the system. Understanding the mapping from local behavior to global behavior is a necessary but insufficient condition for controlling and designing autonomic systems. We must also discover how to exploit the inverse relationship: How can we derive a set of behavioral and interaction rules that, if embedded in individual autonomic elements, will induce a desired global behavior? The nonlinearity of emergent behavior makes such an inversion highly nontrivial. One plausible approach couples advanced search and optimization techniques with parameterized models of the local-to-global relationship and the likely set of environmental influences to which the system will be subjected. Melanie Mitchell and colleagues at the Santa Fe Institute have pioneered this approach, using genetic algorithms to evolve the local transformation rules of simple cellular automata to achieve desired global behaviors.[4] At NASA, David Wolpert and colleagues have studied algorithms that, given a high-level global objective, derive individual goals for individual agents. When each agent selfishly follows its goals, the desired global behavior results.[5] These methods are just a start. We have yet to understand fundamental limits on what classes of global behavior can be achieved, nor do we have practical methods for designing emergent system behavior. Moreover, although these methods establish the rules of a system at design time, autonomic systems must deal with shifting conditions that can be known only at runtime. Control-theoretic approaches may prove useful in this capacity; some autonomic managers may use control systems to govern the behavior of their associated managed elements. The greatest value may be in extending distributed or hierarchical control theories, which consider interactions among independently or hierarchically controlled elements, rather than focusing on an individual controlled element. Newer paradigms for control may be needed when there is no clear separation of scope or time scale. Robustness Theory A related challenge is to develop a theory of robustness for autonomic systems, including definitions and analyses of robustness, diversity, redundancy, and optimality and their relationship to one another. The Santa Fe Institute recently began a multidisciplinary study on this topic. Learning and Optimization Theory Machine learning by a single agent in relatively static environments is well-studied and well-supported by strong theoretical results. However, in more sophisticated autonomic systems, individual elements will be agents that continually adapt to their environment—an environment that consists largely of other agents. Thus, even with stable external conditions, agents are adapting to one another, which violates the traditional assumptions on which single-agent learning theories are based. There are no guarantees of convergence. In fact, interesting forms of instability have been observed in such cases. Learning in multiagent systems is a challenging but relatively unexplored problem, with virtually no major theorems and only a handful of empirical results. Just as learning becomes a more challenging problem in multiagent systems, so does optimization. The root cause is the same—whether it is because they are learning or because they are optimizing, agents are changing their behavior, making it necessary for other agents to change their behavior, potentially leading to instabilities. Optimization in such an environment must deal with dynamics created by a collective mode of oscillation rather than a drifting environmental signal. Optimization techniques that assume a stationary environment have been observed to fail pathologically in multiagent systems; therefore, they must either be revamped or replaced with new methods. Negotiation Theory A solid theoretical foundation for negotiation must take into account two perspectives. From the perspective of individual elements, we must develop and analyze algorithms and negotiation protocols and determine what bidding or negotiation algorithms are most effective. From the perspective of the system as a whole, we must establish how overall system behavior depends on the mixture of negotiation algorithms that various autonomic elements use, and establish the conditions under which multilateral—as opposed to bilateral—negotiations among elements are necessary or desirable. Automated Statistical Modeling Statistical models of large networked systems will let autonomic elements or systems detect or predict overall performance problems from a stream of sensor data from individual devices. At long time scales—during which the configuration of the system changes—we seek methods that automate the aggregation of statistical variables to reduce the dimensionality of the problem to a size that is amenable to adaptive learning and optimization techniques that operate on shorter time scales. Is it possible to meet the grand challenge of autonomic computing without magic and without fully solving the AI problem? I believe it is, but it will take time and patience. Long before many of the more challenging problems are solved, less automated realizations of autonomic systems will be extremely valuable, and their value will increase substantially as autonomic computing technology improves and earns greater trust and acceptance. A vision this large requires that we pool expertise in many areas of computer science as well as in disciplines that lie far beyond computing traditional boundaries. We must look to scientists studying nonlinear dynamics and complexity for new theories of emergent phenomena and robustness. We must look to economists and e-commerce researchers for ideas and technologies about negotiation and supply webs. We must look to psychologists and human factors researchers for new goal-definition and visualization paradigms and for ways to help humans build trust in autonomic systems. We must look to the legal profession, since many of the same issues that arise in the context of e-commerce will be important in autonomic systems that span organizational or national boundaries. Bridging the language and cultural divides among the many disciplines needed for this endeavor and harnessing the diversity to yield successful and perhaps universal approaches to autonomic computing will perhaps be the greatest challenge. It will be interesting to see what new cross-disciplines develop as we begin to work together to solve these fundamental problems. | 
