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Computing Plan-Length Bounds Using Lengths of Longest Paths [article]

Mohammad Abdulaziz, Dominik Berger
2021 arXiv   pre-print
We devise a method to exactly compute the length of the longest simple path in factored state spaces, like state spaces encountered in classical planning.  ...  Although the complexity of this problem is NEXP-Hard, we show that our method can be used to compute practically useful upper-bounds on lengths of plans.  ...  Compositional bounding methods compute an upper bound on a factored transition system's diameter by composing together values of topological properties of state spaces of abstract subsystems (Baumgartner  ... 
arXiv:2006.01011v2 fatcat:khlvh623lfa75dwql3vq4eui3e

Plan-Length Bounds: Beyond 1-Way Dependency

Mohammad Abdulaziz
2019 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We consider the problem of compositionally computing upper bounds on lengths of plans.  ...  Following existing work, our approach is based on a decomposition of state-variable dependency graphs (a.k.a. causal graphs).  ...  Michael Norrish, Lars Hupel and Simon Wimmer for proofreading parts of this paper, and Lars Hupel for helping me set up the experiments. We also thank Prof.  ... 
doi:10.1609/aaai.v33i01.33017502 fatcat:rd3sc6ingzbftaijl6ugkdziym

On the Completeness of Bounded Model Checking for Threshold-Based Distributed Algorithms: Reachability [chapter]

Igor Konnov, Helmut Veith, Josef Widder
2014 Lecture Notes in Computer Science  
We show that the diameters of accelerated counter systems of FTDAs, and of their counter abstractions, have a quadratic upper bound in the number of local transitions.  ...  To ensure completeness, we need an upper bound on the diameter, i.e., on the longest distance between states.  ...  However, in [2] a transition is chosen and accelerated dynamically in the course of symbolic state space exploration, while we statically use acceleration factors and reordering of transitions.  ... 
doi:10.1007/978-3-662-44584-6_10 fatcat:mmk4jaofj5gvrpq52l64skhjoq

Quantum box fabrication tolerance and size limits in semiconductors and their effect on optical gain

K.J. Vahala
1988 IEEE Journal of Quantum Electronics  
Lower and upper limits on size are established for quantum boxes. The lower limit is shown to result from a critical size below which bound electronic states no longer exist.  ...  The optical gain of arrays of quantum boxes is computed taking into account the inhomogenous broadening of the gain spectrum resulting from fabricational variations in quantum box size and shape.  ...  The upper limit is set by the need to create a "discrete" state space in at least one of the energy bands.  ... 
doi:10.1109/3.157 fatcat:n3wtjtvxdzc2hngj42zxxcerhu

Improved Exploration in Factored Average-Reward MDPs [article]

Mohammad Sadegh Talebi, Anders Jonsson, Odalric-Ambrym Maillard
2021 arXiv   pre-print
More specifically, we consider an FMDP where the state-action space 𝒳 and the state-space 𝒮 admit the respective factored forms of 𝒳 = ⊗_i=1^n 𝒳_i and 𝒮=⊗_i=1^m 𝒮_i, and the transition and reward  ...  We further show that when the factorization structure corresponds to the Cartesian product of some base MDPs, the regret of DBN-UCRL is upper bounded by the sum of regret of the base MDPs.  ...  Odalric-Ambrym Maillard is supported by CPER Nord-Pas-de-Calais/FEDER DATA Advanced data science and technologies 2015-2020, the French Ministry of Higher Education and Research, Inria, Inria Scool, the  ... 
arXiv:2009.04575v3 fatcat:lxoxlrzo5rgbbii7ciufwk4knu

A Survey of Optimistic Planning in Markov Decision Processes [chapter]

Lucian Buşoniu, Rémi Munos, Robert Babuška
2013 Reinforcement Learning and Approximate Dynamic Programming for Feedback Control  
The space of planning policies is explored optimistically, focusing on areas with largest upper bounds on the value -or upper confidence bounds, in the stochastic case.  ...  At each discrete time step, these algorithms maximize the predicted value of planning policies from the current state, and apply the first action of the best policy found.  ...  Lipschitz functions defined over arbitrary metric spaces, will combine the two types of optimism highlighted above: upper confidence bounds due to the stochastic samples, with diameter-related bounds  ... 
doi:10.1002/9781118453988.ch22 fatcat:ix4pbp4qpvc2lp44ckd63o3xa4

On the completeness of bounded model checking for threshold-based distributed algorithms: Reachability

Igor Konnov, Helmut Veith, Josef Widder
2017 Information and Computation  
We show that the diameters of accelerated counter systems of FTDAs, and of their counter abstractions, have a quadratic upper bound in the number of local transitions.  ...  Due to state space explosion, applying this technique to distributed algorithms with hundreds of local states is challenging for state-of-the-art model checkers.  ...  However, in [1] a transition is chosen and accelerated dynamically in the course of symbolic state space exploration, while we use acceleration factors and reordering to construct a bound as a formula  ... 
doi:10.1016/j.ic.2016.03.006 fatcat:txsob4a4tbbfto6qxtxyeg5gea

A Unified Analysis of Dynamic Interactive Learning [article]

Xing Gao, Thomas Maranzatto, Lev Reyzin
2022 arXiv   pre-print
Using this general model we solve the open problem of closing the gap between the upper and lower bounds on query complexity.  ...  diameter graphs by using a Markov Chain model.  ...  We want to find the worst case query upper bound, which can be used as a benchmark when modeling various types of transitions.  ... 
arXiv:2204.07071v1 fatcat:mm7x6iqsizeoxgx3cj54p4txv4

Near-optimal Reinforcement Learning in Factored MDPs [article]

Ian Osband, Benjamin Van Roy
2014 arXiv   pre-print
state and action spaces.  ...  We provide two algorithms that satisfy near-optimal regret bounds in this context: posterior sampling reinforcement learning (PSRL) and an upper confidence bound algorithm (UCRL-Factored).  ...  Acknowledgments Osband is supported by Stanford Graduate Fellowships courtesy of PACCAR inc. This work was supported in part by Award CMMI-0968707 from the National Science Foundation.  ... 
arXiv:1403.3741v3 fatcat:uwg5fer5jjdyrecz6ns4yde7ti

Optimistic planning for continuous-action deterministic systems

Lucian Busoniu, Alexander Daniels, Remi Munos, Robert Babuska
2013 2013 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL)  
SOOP is the first method to explore the true solution space, consisting of infinite sequences of continuous actions, without requiring knowledge about the smoothness of the system.  ...  We introduce a novel planning algorithm called SOOP that works for deterministic systems with continuous states and actions.  ...  The system state changes according to x ′ = f (x, u), where f : X ×U → X is the transition function, and the quality of transitions is measured by the bounded reward function r(x, u, x ′ ), where r : X  ... 
doi:10.1109/adprl.2013.6614991 dblp:conf/adprl/BusoniuDMB13 fatcat:em4v6xs5zjcwtbs7oc6hub4wsq

Complexity of Model Checking MDPs against LTL Specifications

Dileep Kini, Mahesh Viswanathan, Marc Herbstritt
2018 Foundations of Software Technology and Theoretical Computer Science  
In this paper we study the precise complexity of these problems when the specification is constrained to be in different fragments of LTL.  ...  Given a Markov Decision Process (MDP) M, an LTL formula ϕ, and a threshold θ ∈ [0, 1], the verification question is to determine if there is a scheduler with respect to which the executions of M satisfying  ...  For the other upper bounds in Table 1 , we present a new space efficient algorithm to compute the probability of repeatedly visiting a set of states in Markov chains of small diameter; this result mimics  ... 
doi:10.4230/lipics.fsttcs.2017.35 dblp:conf/fsttcs/KiniV17 fatcat:6wlwfxnc3jdzxhs3o7j3jh5tqm

On the jamming phase diagram for frictionless hard-sphere packings

Vasili Baranau, Ulrich Tallarek
2014 Soft Matter  
When 4 reaches the ideal glass transition density 4 g , 4 J reaches the ideal glass density (the glass close packing limit) 4 GCP , so that the available phase space is dominated at 4 g by the basin of  ...  We computer-generated monodisperse and polydisperse frictionless hard-sphere packings of 10 4 particles with log-normal particle diameter distributions in a wide range of packing densities 4 (for monodisperse  ...  This denition is unsuitable in the light of the current results, as the states in closed liquid bounding regions (that dominate the phase space for 4 # 4 MCT ) would be called glassy as well. C.  ... 
doi:10.1039/c4sm01439a pmid:25155116 fatcat:4uwn3kk6mrdxxlutq4jirhpofy

$$2^5$$ Years of Model Checking [chapter]

Edmund M. Clarke, Qinsi Wang
2015 Lecture Notes in Computer Science  
Model Checking is an automatic verification technique for large state transition systems. It was originally developed for reasoning about finite-state concurrent systems.  ...  number of states.  ...  It has been shown that the diameter (i.e., the longest shortest path between any two states) of the state-transition system could be used as an upper bound [9] .  ... 
doi:10.1007/978-3-662-46823-4_2 fatcat:g4tbd7fribgothf2bfgajkywfe

Page 6740 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
Under certain assumptions on the rate function of the arrival process, we show that the upper bound is tight.  ...  As an application of this result, we then consider a priority queueing system with two queues. Using the earlier result, we derive an upper bound on the tail probability of the delay.  ... 

Maximum Expected Hitting Cost of a Markov Decision Process and Informativeness of Rewards [article]

Falcon Z. Dai, Matthew R. Walter
2019 arXiv   pre-print
We show that this parameter replaces diameter in the upper bound on the optimal value span of an extended MDP, thus refining the associated upper bounds on the regret of several UCRL2-like algorithms.  ...  We further establish that shaping can reduce or increase MEHC by at most a factor of two in a large class of MDPs with finite MEHC and unsaturated optimal average rewards.  ...  the actual MDP (Definition 1), S the size of the state space, and A the size of the action space.  ... 
arXiv:1907.02114v2 fatcat:t4ww5sohz5ds7iy2p6dlyuewrm
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