3,741 research outputs found
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
The Spectrum of Strong Behavioral Equivalences for Nondeterministic and Probabilistic Processes
We present a spectrum of trace-based, testing, and bisimulation equivalences
for nondeterministic and probabilistic processes whose activities are all
observable. For every equivalence under study, we examine the discriminating
power of three variants stemming from three approaches that differ for the way
probabilities of events are compared when nondeterministic choices are resolved
via deterministic schedulers. We show that the first approach - which compares
two resolutions relatively to the probability distributions of all considered
events - results in a fragment of the spectrum compatible with the spectrum of
behavioral equivalences for fully probabilistic processes. In contrast, the
second approach - which compares the probabilities of the events of a
resolution with the probabilities of the same events in possibly different
resolutions - gives rise to another fragment composed of coarser equivalences
that exhibits several analogies with the spectrum of behavioral equivalences
for fully nondeterministic processes. Finally, the third approach - which only
compares the extremal probabilities of each event stemming from the different
resolutions - yields even coarser equivalences that, however, give rise to a
hierarchy similar to that stemming from the second approach.Comment: In Proceedings QAPL 2013, arXiv:1306.241
On overfitting and asymptotic bias in batch reinforcement learning with partial observability
This paper provides an analysis of the tradeoff between asymptotic bias
(suboptimality with unlimited data) and overfitting (additional suboptimality
due to limited data) in the context of reinforcement learning with partial
observability. Our theoretical analysis formally characterizes that while
potentially increasing the asymptotic bias, a smaller state representation
decreases the risk of overfitting. This analysis relies on expressing the
quality of a state representation by bounding L1 error terms of the associated
belief states. Theoretical results are empirically illustrated when the state
representation is a truncated history of observations, both on synthetic POMDPs
and on a large-scale POMDP in the context of smartgrids, with real-world data.
Finally, similarly to known results in the fully observable setting, we also
briefly discuss and empirically illustrate how using function approximators and
adapting the discount factor may enhance the tradeoff between asymptotic bias
and overfitting in the partially observable context.Comment: Accepted at the Journal of Artificial Intelligence Research (JAIR) -
31 page
Deciding the value 1 problem for probabilistic leaktight automata
The value 1 problem is a decision problem for probabilistic automata over
finite words: given a probabilistic automaton, are there words accepted with
probability arbitrarily close to 1? This problem was proved undecidable
recently; to overcome this, several classes of probabilistic automata of
different nature were proposed, for which the value 1 problem has been shown
decidable. In this paper, we introduce yet another class of probabilistic
automata, called leaktight automata, which strictly subsumes all classes of
probabilistic automata whose value 1 problem is known to be decidable. We prove
that for leaktight automata, the value 1 problem is decidable (in fact,
PSPACE-complete) by constructing a saturation algorithm based on the
computation of a monoid abstracting the behaviours of the automaton. We rely on
algebraic techniques developed by Simon to prove that this abstraction is
complete. Furthermore, we adapt this saturation algorithm to decide whether an
automaton is leaktight. Finally, we show a reduction allowing to extend our
decidability results from finite words to infinite ones, implying that the
value 1 problem for probabilistic leaktight parity automata is decidable
Quantifying Information Leakage of Randomized Protocols
International audienceThe quantification of information leakage provides a quantitative evaluation of the security of a system. We propose the usage of Markovian processes to model and analyze the information leakage of deterministic and probabilistic systems. We show that this method generalizes the lattice of information approach and is a natural framework for modeling refined attackers capable to observe the internal behavior of the system. We also use our method to obtain an algorithm for the computation of channel capacity from our Markovian models. Finally, we show how to use the method to analyze timed and non-timed attacks on the Onion Routing protocol
Rate-Based Transition Systems for Stochastic Process Calculi
A variant of Rate Transition Systems (RTS), proposed by Klin and Sassone, is introduced and used as the basic model for defining stochastic behaviour of processes. The transition relation used in our variant associates to each process, for each action, the set of possible futures paired with a measure indicating their rates. We show how RTS can be used for providing the operational semantics of stochastic extensions of classical formalisms, namely CSP and CCS. We also show that our semantics for stochastic CCS guarantees associativity of parallel composition. Similarly, in contrast with the original definition by Priami, we argue that a semantics for stochastic π-calculus can be provided that guarantees associativity of parallel composition
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