Cost analysis of nondeterministic probabilistic programs

Wang, Peixin; Fu, Hongfei; Goharshady, Amir Kafshdar; Chatterjee, Krishnendu; Qin, Xudong; Shi, Wenjun

doi:10.1145/3314221.3314581

Cited by 40 publications

(58 citation statements)

References 75 publications

(89 reference statements)

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“…Reasoning About Probabilistic Programs. There exist several works on automatic expected cost analysis of sequential (imperative) probabilistic programs [Chatterjee et al 2016;Kura et al 2019;Ngo et al 2018;Wang et al 2019a]. They can derive symbolic polynomial bounds and can be seen as an automation of Kozen's weakest pre-expectation caclulus Kozen 1981].…”

Section: Related Workmentioning

confidence: 99%

“…The newly designed AARA for PRast has interesting and non-trivial interactions with probabilistic channels that enable a more compositional analysis resulting in precise bounds. While there are several techniques for automatic expected cost analysis of sequential probabilistic programs [Chatterjee et al 2016;Ngo et al 2018;Wang et al 2019a], we are only aware of manual rule-based reasoning systems [McIver et al 2016;Tassarotti and Harper 2019] or probabilistic model checking techniques for analyzing cost of concurrent probabilistic programs.…”

Section: Introductionmentioning

confidence: 99%

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Work Analysis with Resource-Aware Session Types

Das

Hoffmann

Pfenning

2018

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science

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While there exist several successful techniques for supporting programmers in deriving static resource bounds for sequential code, analyzing the resource usage of message-passing concurrent processes poses additional challenges. To meet these challenges, this article presents an analysis for statically deriving worst-case bounds on the total work performed by message-passing processes. To decompose interacting processes into components that can be analyzed in isolation, the analysis is based on novel resource-aware session types, which describe protocols and resource contracts for inter-process communication. A key innovation is that both messages and processes carry potential to share and amortize cost while communicating. To symbolically express resource usage in a setting without static data structures and intrinsic sizes, resource contracts describe bounds that are functions of interactions between processes. Resource-aware session types combine standard binary session types and type-based amortized resource analysis in a linear type system. This type system is formulated for a core session-type calculus of the language SILL and proved sound with respect to a multiset-based operational cost semantics that tracks the total number of messages that are exchanged in a system. The effectiveness of the analysis is demonstrated by analyzing standard examples from amortized analysis and the literature on session types and by a comparative performance analysis of different concurrent programs implementing the same interface. arXiv:1712.08310v2 [cs.PL] 27 Apr 2018components that can be analyzed in isolation. After all, the resource usage of each component crucially depends on its interactions with the world.In this paper, we study the foundations of worst-case resource analysis for message-passing processes. A key idea of our approach is to rely on resourceaware session types to describe structure, protocols, and resource bounds for inter-process communication that we can use to perform a compositional and precise amortized analysis. Session types [32,33,12,13,45] prescribe bidirectional communication protocols for message-passing processes. Binary session types govern the interaction of two processes along a single channel, prescribing complementary send and receive actions for the processes at the two endpoints of a channel. We use such protocols as the basis of resource usage contracts that not only specify the type but also the potential of a message that is sent along a channel. The potential (in the sense of classic amortized analysis [43]) may be spent sending other messages as part of the network of interacting processes, or maintained locally for future interactions. Resource analysis is static, using the type system, and the runtime behavior of programs is not affected.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Work Analysis with Resource-Aware Session Types

Das

Hoffmann

Pfenning

2018

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science

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“…In previous results such as [Chakarov and Sankaranarayanan 2013;Chatterjee et al 2018c], martingales have been successfully applied to prove termination properties of probabilistic programs. Besides qualitative termination properties, martingales can also derive tight quantitative upper/lower bounds for expected termination time and resource usage [Chatterjee et al 2018a,c;Ngo et al 2018;Wang et al 2019]. In this paper, we utilize the quantitative feature of martingales to bound the difference caused by non-synchronous situations.…”

Section: Proving Expected Sensitivity For Non-expansive Simple Loopsmentioning

confidence: 99%

“…We consider examples and their variants from the literature [Abate et al 2010;Chatterjee et al 2018b,c;Ngo et al 2018;Wang et al 2019]. Single/double-room heating is from [Abate et al 2010].…”

Section: Experimental Examplesmentioning

confidence: 99%

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Proving expected sensitivity of probabilistic programs with randomized variable-dependent termination time

Wang

Chatterjee

et al. 2019

Proc. ACM Program. Lang.

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The notion of program sensitivity (aka Lipschitz continuity) specifies that changes in the program input result in proportional changes to the program output. For probabilistic programs the notion is naturally extended to expected sensitivity. A previous approach develops a relational program logic framework for proving expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded. In this work, we consider probabilistic while loops where the number of iterations is not fixed, but randomized and depends on the initial input values. We present a sound approach for proving expected sensitivity of such programs. Our sound approach is martingale-based and can be automated through existing martingale-synthesis algorithms. Furthermore, our approach is compositional for sequential composition of while loops under a mild side condition. We demonstrate the effectiveness of our approach on several classical examples from Gambler's Ruin, stochastic hybrid systems and stochastic gradient descent. We also present experimental results showing that our automated approach can handle various probabilistic programs in the literature.

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Exponential Automatic Amortized Resource Analysis

Kahn

Hoffmann

2020

Lecture Notes in Computer Science

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Automatic amortized resource analysis (AARA) is a typebased technique for inferring concrete (non-asymptotic) bounds on a program's resource usage. Existing work on AARA has focused on bounds that are polynomial in the sizes of the inputs. This paper presents and extension of AARA to exponential bounds that preserves the benefits of the technique, such as compositionality and efficient type inference based on linear constraint solving. A key idea is the use of the Stirling numbers of the second kind as the basis of potential functions, which play the same role as the binomial coefficients in polynomial AARA. To formalize the similarities with the existing analyses, the paper presents a general methodology for AARA that is instantiated to the polynomial version, the exponential version, and a combined system with potential functions that are formed by products of Stirling numbers and binomial coefficients. The soundness of exponential AARA is proved with respect to an operational cost semantics and the analysis of representative example programs demonstrates the effectiveness of the new analysis.

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Cost analysis of nondeterministic probabilistic programs

Cited by 40 publications

References 75 publications

Work Analysis with Resource-Aware Session Types

Work Analysis with Resource-Aware Session Types

Proving expected sensitivity of probabilistic programs with randomized variable-dependent termination time

Exponential Automatic Amortized Resource Analysis

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