Active inference, evidence accumulation, and the urn task

Deciding how much evidence to accumulate before making a decision is a problem we and other animals often face, but one that is not completely understood. This issue is particularly important because a tendency to sample less information (often known as reflection impulsivity) is a feature in several psychopathologies, such as psychosis. A formal understanding of information sampling may therefore clarify the computational anatomy of psychopathology. In this theoretical letter, we consider evidence accumulation in terms of active (Bayesian) inference using a generic model of Markov decision processes. Here, agents are equipped with beliefs about their own behavior--in this case, that they will make informed decisions. Normative decision making is then modeled using variational Bayes to minimize surprise about choice outcomes. Under this scheme, different facets of belief updating map naturally onto the functional anatomy of the brain (at least at a heuristic level). Of particular interest is the key role played by the expected precision of beliefs about control, which we have previously suggested may be encoded by dopaminergic neurons in the midbrain. We show that manipulating expected precision strongly affects how much information an agent characteristically samples, and thus provides a possible link between impulsivity and dopaminergic dysfunction. Our study therefore represents a step toward understanding evidence accumulation in terms of neurobiologically plausible Bayesian inference and may cast light on why this process is disordered in psychopathology

Needs and challenges for assessing the environmental impacts of engineered nanomaterials (ENMs).

The potential environmental impact of nanomaterials is a critical concern and the ability to assess these potential impacts is top priority for the progress of sustainable nanotechnology. Risk assessment tools are needed to enable decision makers to rapidly assess the potential risks that may be imposed by engineered nanomaterials (ENMs), particularly when confronted by the reality of limited hazard or exposure data. In this review, we examine a range of available risk assessment frameworks considering the contexts in which different stakeholders may need to assess the potential environmental impacts of ENMs. Assessment frameworks and tools that are suitable for the different decision analysis scenarios are then identified. In addition, we identify the gaps that currently exist between the needs of decision makers, for a range of decision scenarios, and the abilities of present frameworks and tools to meet those needs

Use and Communication of Probabilistic Forecasts

Probabilistic forecasts are becoming more and more available. How should they be used and communicated? What are the obstacles to their use in practice? I review experience with five problems where probabilistic forecasting played an important role. This leads me to identify five types of potential users: Low Stakes Users, who don't need probabilistic forecasts; General Assessors, who need an overall idea of the uncertainty in the forecast; Change Assessors, who need to know if a change is out of line with expectatations; Risk Avoiders, who wish to limit the risk of an adverse outcome; and Decision Theorists, who quantify their loss function and perform the decision-theoretic calculations. This suggests that it is important to interact with users and to consider their goals. The cognitive research tells us that calibration is important for trust in probability forecasts, and that it is important to match the verbal expression with the task. The cognitive load should be minimized, reducing the probabilistic forecast to a single percentile if appropriate. Probabilities of adverse events and percentiles of the predictive distribution of quantities of interest seem often to be the best way to summarize probabilistic forecasts. Formal decision theory has an important role, but in a limited range of applications

Technical Report: Distribution Temporal Logic: Combining Correctness with Quality of Estimation

We present a new temporal logic called Distribution Temporal Logic (DTL) defined over predicates of belief states and hidden states of partially observable systems. DTL can express properties involving uncertainty and likelihood that cannot be described by existing logics. A co-safe formulation of DTL is defined and algorithmic procedures are given for monitoring executions of a partially observable Markov decision process with respect to such formulae. A simulation case study of a rescue robotics application outlines our approach.Comment: More expanded version of "Distribution Temporal Logic: Combining Correctness with Quality of Estimation" to appear in IEEE CDC 201

Probabilistic Opacity for Markov Decision Processes

Opacity is a generic security property, that has been defined on (non probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an external observer, the value of interest for opacity is a measure of the set of runs disclosing the secret. We extend this definition to the richer framework of Markov decision processes, where non deterministic choice is combined with probabilistic transitions, and we study related decidability problems with partial or complete observation hypotheses for the schedulers. We prove that all questions are decidable with complete observation and $\omega$-regular secrets. With partial observation, we prove that all quantitative questions are undecidable but the question whether a system is almost surely non opaque becomes decidable for a restricted class of $\omega$-regular secrets, as well as for all $\omega$-regular secrets under finite-memory schedulers

Randomness for Free

We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (both players interact simultaneously); and (b) turn-based (both players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. In this work we present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games

Planning in probabilistic domains using a deterministic numeric planner

In the probabilistic track of the IPC5 - the last International planning competitions - a probabilistic planner based on combining deterministic planning with replanning - FF-REPLAN - out performed the other competitors. This probabilistic planning paradigm discarded the probabilistic information of the domain, just considering for each action its nominal effect as a deterministic effect

Probabilistic Bisimulation: Naturally on Distributions

In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a long-standing open problem concerning the representation of memoryless continuous time by memory-full continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems