Prakash Panangaden

Publications

Tensor of Quantitative Equational Theories.

Giorgio Bacci

Radu Mardare

Gordon Plotkin

2020-12-31

CALCO (published)

qu an tph ] 10 O ct 2 01 1 Quantum Communication in Rindler Spacetime

Kamil Brádler

P. Hayden

A state that an inertial observer in Minkowski space perceiv es to be the vacuum will appear to an accelerating observer to be a thermal ba … (see more)th of radiation. We study the impact of this Davies-Fulling-Unruh noise on comm unication, particularly quantum communication from an inertial sender to an ac celerating observer and private communication between two inertial observers i n the presence of an accelerating eavesdropper. In both cases, we establish com pact, tractable formulas for the associated communication capacities assuming enco dings that allow a single excitation in one of a fixed number of modes per use of the co mmunications channel. Our contributions include a rigorous presentatio n of the general theory of the private quantum capacity as well as a detailed analysis o f the structure of these channels, including their group-theoretic properties and proof that they are conjugate degradable. Connections between the Unruh channel a d optical amplifiers are also discussed.

2020-12-31

(published)

www.semanticscholar.org

Quantitative Equational Reasoning

Giorgio Bacci

Radu Mardare

Gordon Plotkin

Equational logic is central to reasoning about programs.What is the right equational setting for reasoning about probabilistic programs? It … (see more)has been understood that instead of equivalence relations one should work with (pseudo)metrics in a probabilistic setting. However, it is not clear how this relates to equational reasoning. In recent work the notion of a quantitative equational logic was introduced and developed. This retains many of the features of ordinary logic but fits naturally with metric reasoning. The present chapter is an elementry introduction to this topic. In this setting one can define analogues of algebras and free algebras. It turns out that the Kantorovich (Wasserstein) metric emerges as a free construction from a simple quantitative equational theory. We give a couple of examples of quantitative analogues of familiar effects from programming language theory. We do not assume any background in equational logic or advanced category theory.

2020-12-02

Foundations of Probabilistic Programming (published)

Universal Semantics for the Stochastic Lambda-Calculus

Pedro H. Azevedo de Amorim

Dexter Kozen

Radu Mardare

Michael Roberts

We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build … (see more)on previous work that used similar techniques to reason about higher-order probabilistic programs, but for the first time admit an adequacy theorem relating the operational and denotational views. This resolves the main issue left open in (Bacci et al. 2018).

2020-11-28

arXiv.org (preprint)

dblp.uni-trier.de

Latent Variable Modelling with Hyperbolic Normalizing Flows

Avishek Joey Bose

Ariella Smofsky

Renjie Liao

William L. Hamilton

The choice of approximate posterior distributions plays a central role in stochastic variational inference (SVI). One effective solution is … (see more)the use of normalizing flows \cut{defined on Euclidean spaces} to construct flexible posterior distributions. However, one key limitation of existing normalizing flows is that they are restricted to the Euclidean space and are ill-equipped to model data with an underlying hierarchical structure. To address this fundamental limitation, we present the first extension of normalizing flows to hyperbolic spaces. We first elevate normalizing flows to hyperbolic spaces using coupling transforms defined on the tangent bundle, termed Tangent Coupling (

2020-11-20

Proceedings of the 37th International Conference on Machine Learning (published)

proceedings.mlr.press

A Study of Policy Gradient on a Class of Exactly Solvable Models

Gavin McCracken

Colin Daniels

Rosie Zhao

Anna M. Brandenberger

Policy gradient methods are extensively used in reinforcement learning as a way to optimize expected return. In this paper, we explore the e… (see more)volution of the policy parameters, for a special class of exactly solvable POMDPs, as a continuous-state Markov chain, whose transition probabilities are determined by the gradient of the distribution of the policy's value. Our approach relies heavily on random walk theory, specifically on affine Weyl groups. We construct a class of novel partially observable environments with controllable exploration difficulty, in which the value distribution, and hence the policy parameter evolution, can be derived analytically. Using these environments, we analyze the probabilistic convergence of policy gradient to different local maxima of the value function. To our knowledge, this is the first approach developed to analytically compute the landscape of policy gradient in POMDPs for a class of such environments, leading to interesting insights into the difficulty of this problem.

2020-11-02

ArXiv (preprint)

arxiv.org

Towards a Classification of Behavioural Equivalences in Continuous-time Markov Processes

Linan Chen

Florence Clerc

2020-09-30

Mathematical Foundations of Programming Semantics (published)

Minimisation in Logical Form

Nick Bezhanishvili

Marcello M. Bonsangue

Helle Hvid Hansen

Dexter Kozen

C. Kupke

Alexandra Silva

2020-05-22

ArXiv (preprint)

arxiv.org

A Distributional Analysis of Sampling-Based Reinforcement Learning Algorithms

Philip Amortila

Bellemare Marc-Emmanuel

We present a distributional approach to theoretical analyses of reinforcement learning algorithms for constant step-sizes. We demonstrate it… (see more)s effectiveness by presenting simple and unified proofs of convergence for a variety of commonly-used methods. We show that value-based methods such as TD(

2019-12-31

AISTATS (published)

proceedings.mlr.press

Singular Value Automata and Approximate Minimization

Borja Balle

The present paper uses spectral theory of linear operators to construct approximately minimal realizations of weighted languages. Our new co… (see more)ntributions are: (i) a new algorithm for the SVD decomposition of infinite Hankel matrices based on their representation in terms of weighted automata, (ii) a new canonical form for weighted automata arising from the SVD of its corresponding Hankel matrix and (iii) an algorithm to construct approximate minimizations of given weighted automata by truncating the canonical form. We give bounds on the quality of our approximation.

2019-05-26

Mathematical Structures in Computer Science (published)

arxiv.org

Temporally Extended Metrics for Markov Decision Processes.

Philip Amortila

Bellemare Marc-Emmanuel