We propose a new interpretation of spiking neurons as Bayesian integrators accumulatingevidence over time about events in the external world or the body, and communicating to other neurons their certainties about these events. In this model, spikes signal the occurrence of new information, i.e.what cannot be predicted from the past activity. As a result, firing statistics are close to Poisson, albeit providing a deterministic representation ofprobabilities. We proceed to develop a theory of Bayesian inference in spiking neural networks, recurrent interactions implementing avariant of belief propagation. Many perceptual and motor tasks performed by the central nervous system are probabilistic, andcan be described in a Bayesian framework [4, 3].

An analog system-on-Chip for kernel-based pattern Classification and sequence estimation is presented.

Many sequential prediction tasks involve locating instances of patterns insequences. Generative probabilistic language models, such as hidden Markov models (HMMs), have been successfully applied to many of these tasks. A limitation of these models however, is that they cannot naturally handle cases in which pattern instances overlap in arbitrary ways. We present an alternative approach, based on conditional Markov networks, that can naturally represent arbitrarilyoverlapping elements. We show how to efficiently train and perform inference with these models. Experimental results froma genomics domain show that our models are more accurate at locating instances of overlapping patterns than are baseline models based on HMMs.

First-order Markov models have been successfully applied to many problems, forexample in modeling sequential data using Markov chains, and modeling control problems using the Markov decision processes (MDP) formalism. If a first-order Markov model's parameters are estimated from data, the standard maximum likelihood estimator considers only the first-order (single-step) transitions. But for many problems, the firstorder conditionalindependence assumptions are not satisfied, and as a result the higher order transition probabilities may be poorly approximated. Motivated by the problem of learning an MDP's parameters for control, we propose an algorithm for learning a first-order Markov model that explicitly takesinto account higher order interactions during training. Our algorithm uses an optimization criterion different from maximum likelihood, andallows us to learn models that capture longer range effects, but without giving up the benefits of using first-order Markov models. Our experimental results also show the new algorithm outperforming conventional maximumlikelihood estimation in a number of control problems where the MDP's parameters are estimated from data.

We describe the version of the GPT planner used in the probabilistic track of the 4th International Planning Competition (ipc-4). This version, called mGPT, solves Markov Decision Processes specified in the ppddl language by extracting and using different classes of lower bounds along with various heuristic-search algorithms. The lower bounds are extracted from deterministic relaxations where the alternative probabilistic effects of an action are mapped into different, independent, deterministic actions. The heuristic-search algorithms use these lower bounds for focusing the updates and delivering a consistent value function over all states reachable from the initial state and the greedy policy.

We develop and analyze methods for computing provably optimal {\em maximum a posteriori} (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex combination of tree-structured distributions, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in terms of the combined optimal values of the tree problems. We prove that this upper bound is tight if and only if all the tree distributions share an optimal configuration in common. An important implication is that any such shared configuration must also be a MAP configuration for the original distribution. Next we develop two approaches to attempting to obtain tight upper bounds: (a) a {\em tree-relaxed linear program} (LP), which is derived from the Lagrangian dual of the upper bounds; and (b) a {\em tree-reweighted max-product message-passing algorithm} that is related to but distinct from the max-product algorithm. In this way, we establish a connection between a certain LP relaxation of the mode-finding problem, and a reweighted form of the max-product (min-sum) message-passing algorithm.

Partially observable Markov decision processes (POMDPs) form an attractive and principled framework for agent planning under uncertainty. Point-based approximate techniques for POMDPs compute a policy based on a finite set of points collected in advance from the agent's belief space. We present a randomized point-based value iteration algorithm called Perseus. The algorithm performs approximate value backup stages, ensuring that in each backup stage the value of each point in the belief set is improved; the key observation is that a single backup may improve the value of many belief points. Contrary to other point-based methods, Perseus backs up only a (randomly selected) subset of points in the belief set, sufficient for improving the value of each belief point in the set. We show how the same idea can be extended to dealing with continuous action spaces. Experimental results show the potential of Perseus in large scale POMDP problems.

In this paper, we consider Markov Decision Processes (MDPs) with error states. Error states are those states entering which is undesirable or dangerous. We define the risk with respect to a policy as the probability of entering such a state when the policy is pursued. We consider the problem of finding good policies whose risk is smaller than some user-specified threshold, and formalize it as a constrained MDP with two criteria. The first criterion corresponds to the value function originally given. We will show that the risk can be formulated as a second criterion function based on a cumulative return, whose definition is independent of the original value function. We present a model free, heuristic reinforcement learning algorithm that aims at finding good deterministic policies. It is based on weighting the original value function and the risk. The weight parameter is adapted in order to find a feasible solution for the constrained problem that has a good performance with respect to the value function. The algorithm was successfully applied to the control of a feed tank with stochastic inflows that lies upstream of a distillation column. This control task was originally formulated as an optimal control problem with chance constraints, and it was solved under certain assumptions on the model to obtain an optimal solution. The power of our learning algorithm is that it can be used even when some of these restrictive assumptions are relaxed.

This paper extends the framework of partially observable Markov decision processes (POMDPs) to multi-agent settings by incorporating the notion of agent models into the state space. Agents maintain beliefs over physical states of the environment and over models of other agents, and they use Bayesian updates to maintain their beliefs over time. The solutions map belief states to actions. Models of other agents may include their belief states and are related to agent types considered in games of incomplete information. We express the agents' autonomy by postulating that their models are not directly manipulable or observable by other agents. We show that important properties of POMDPs, such as convergence of value iteration, the rate of convergence, and piece-wise linearity and convexity of the value functions carry over to our framework. Our approach complements a more traditional approach to interactive settings which uses Nash equilibria as a solution paradigm. We seek to avoid some of the drawbacks of equilibria which may be non-unique and do not capture off-equilibrium behaviors. We do so at the cost of having to represent, process and continuously revise models of other agents. Since the agent's beliefs may be arbitrarily nested, the optimal solutions to decision making problems are only asymptotically computable. However, approximate belief updates and approximately optimal plans are computable. We illustrate our framework using a simple application domain, and we show examples of belief updates and value functions.

Many current large-scale multiagent team implementations can be characterized as following the ``belief-desire-intention'' (BDI) paradigm, with explicit representation of team plans. Despite their promise, current BDI team approaches lack tools for quantitative performance analysis under uncertainty. Distributed partially observable Markov decision problems (POMDPs) are well suited for such analysis, but the complexity of finding optimal policies in such models is highly intractable. The key contribution of this article is a hybrid BDI-POMDP approach, where BDI team plans are exploited to improve POMDP tractability and POMDP analysis improves BDI team plan performance. Concretely, we focus on role allocation, a fundamental problem in BDI teams: which agents to allocate to the different roles in the team. The article provides three key contributions. First, we describe a role allocation technique that takes into account future uncertainties in the domain; prior work in multiagent role allocation has failed to address such uncertainties. To that end, we introduce RMTDP (Role-based Markov Team Decision Problem), a new distributed POMDP model for analysis of role allocations. Our technique gains in tractability by significantly curtailing RMTDP policy search; in particular, BDI team plans provide incomplete RMTDP policies, and the RMTDP policy search fills the gaps in such incomplete policies by searching for the best role allocation. Our second key contribution is a novel decomposition technique to further improve RMTDP policy search efficiency. Even though limited to searching role allocations, there are still combinatorially many role allocations, and evaluating each in RMTDP to identify the best is extremely difficult. Our decomposition technique exploits the structure in the BDI team plans to significantly prune the search space of role allocations. Our third key contribution is a significantly faster policy evaluation algorithm suited for our BDI-POMDP hybrid approach. Finally, we also present experimental results from two domains: mission rehearsal simulation and RoboCupRescue disaster rescue simulation.