Simple Doubly-Efficient Interactive Proof Systems for Locally-Characterizable Sets

A proof system is called doubly-efficient if the prescribed prover strategy can be implemented in polynomial-time and the verifier\u27s strategy can be implemented in almost-linear-time. We present direct constructions of doubly-efficient interactive proof systems for problems in P that are believed to have relatively high complexity. Specifically, such constructions are presented for t-CLIQUE and t-SUM. In addition, we present a generic construction of such proof systems for a natural class that contains both problems and is in NC (and also in SC). The proof systems presented by us are significantly simpler than the proof systems presented by Goldwasser, Kalai and Rothblum (JACM, 2015), let alone those presented by Reingold, Rothblum, and Rothblum (STOC, 2016), and can be implemented using a smaller number of rounds

Tree Codes Improve Convergence Rate of Consensus Over Erasure Channels

We study the problem of achieving average consensus between a group of agents over a network with erasure links. In the context of consensus problems, the unreliability of communication links between nodes has been traditionally modeled by allowing the underlying graph to vary with time. In other words, depending on the realization of the link erasures, the underlying graph at each time instant is assumed to be a subgraph of the original graph. Implicit in this model is the assumption that the erasures are symmetric: if at time t the packet from node i to node j is dropped, the same is true for the packet transmitted from node j to node i. However, in practical wireless communication systems this assumption is unreasonable and, due to the lack of symmetry, standard averaging protocols cannot guarantee that the network will reach consensus to the true average. In this paper we explore the use of channel coding to improve the performance of consensus algorithms. For symmetric erasures, we show that, for certain ranges of the system parameters, repetition codes can speed up the convergence rate. For asymmetric erasures we show that tree codes (which have recently been designed for erasure channels) can be used to simulate the performance of the original "unerased" graph. Thus, unlike conventional consensus methods, we can guarantee convergence to the average in the asymmetric case. The price is a slowdown in the convergence rate, relative to the unerased network, which is still often faster than the convergence rate of conventional consensus algorithms over noisy links

Counterfactual Risk Minimization: Learning from Logged Bandit Feedback

We develop a learning principle and an efficient algorithm for batch learning from logged bandit feedback. This learning setting is ubiquitous in online systems (e.g., ad placement, web search, recommendation), where an algorithm makes a prediction (e.g., ad ranking) for a given input (e.g., query) and observes bandit feedback (e.g., user clicks on presented ads). We first address the counterfactual nature of the learning problem through propensity scoring. Next, we prove generalization error bounds that account for the variance of the propensity-weighted empirical risk estimator. These constructive bounds give rise to the Counterfactual Risk Minimization (CRM) principle. We show how CRM can be used to derive a new learning method -- called Policy Optimizer for Exponential Models (POEM) -- for learning stochastic linear rules for structured output prediction. We present a decomposition of the POEM objective that enables efficient stochastic gradient optimization. POEM is evaluated on several multi-label classification problems showing substantially improved robustness and generalization performance compared to the state-of-the-art.Comment: 10 page

Efficient Batch Verification for UP

Consider a setting in which a prover wants to convince a verifier of the correctness of k NP statements. For example, the prover wants to convince the verifier that k given integers N_1,...,N_k are all RSA moduli (i.e., products of equal length primes). Clearly this problem can be solved by simply having the prover send the k NP witnesses, but this involves a lot of communication. Can interaction help? In particular, is it possible to construct interactive proofs for this task whose communication grows sub-linearly with k? Our main result is such an interactive proof for verifying the correctness of any k UP statements (i.e., NP statements that have a unique witness). The proof-system uses only a constant number of rounds and the communication complexity is k^delta * poly(m), where delta>0 is an arbitrarily small constant, m is the length of a single witness, and the poly term refers to a fixed polynomial that only depends on the language and not on delta. The (honest) prover strategy can be implemented in polynomial-time given access to the k (unique) witnesses. Our proof leverages "interactive witness verification" (IWV), a new type of proof-system that may be of independent interest. An IWV is a proof-system in which the verifier needs to verify the correctness of an NP statement using: (i) a sublinear number of queries to an alleged NP witness, and (ii) a short interaction with a powerful but untrusted prover. In contrast to the setting of PCPs and Interactive PCPs, here the verifier only has access to the raw NP witness, rather than some encoding thereof

Collaborative Verification-Driven Engineering of Hybrid Systems

Hybrid systems with both discrete and continuous dynamics are an important model for real-world cyber-physical systems. The key challenge is to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Often, hybrid systems are rather complex in that they require expertise from many domains (e.g., robotics, control systems, computer science, software engineering, and mechanical engineering). Moreover, despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires nontrivial human guidance, since hybrid systems verification tools solve undecidable problems. It is, thus, not uncommon for development and verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) graphical (UML) and textual modeling of hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks