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We introduce a new constrained optimization method for policy gradient reinforcement learning, which uses two trust regions to regulate each policy update. In addition to using the proximity of one single old policy as the first trust region as done by prior works, we propose to form a second trust region through the construction of another virtual policy that represents a wide range of past policies. We then enforce the new policy to stay closer to the virtual policy, which is beneficial in case the old policy performs badly. More importantly, we propose a mechanism to automatically build the virtual policy from a memory buffer of past policies, providing a new capability for dynamically selecting appropriate trust regions during the optimization process. Our proposed method, dubbed as Memory-Constrained Policy Optimization (MCPO), is examined on a diverse suite of environments including robotic locomotion control, navigation with sparse rewards and Atari games, consistently demonstrating competitive performance against recent on-policy constrained policy gradient methods.

Music source separation with both paired mixed signals and source signals has obtained substantial progress over the years. However, this setting highly relies on large amounts of paired data. Source-only supervision decouples the process of learning a mapping from a mixture to particular sources into a two stage paradigm: source modeling and separation. Recent systems under source-only supervision either achieve good performance in synthetic toy experiments or limited performance in music separation task. In this paper, we leverage flow-based implicit generators to train music source priors and likelihood based objective to separate music mixtures. Experiments show that in singing voice and music separation tasks, our proposed systems achieve competitive results to one of the full supervision systems. We also demonstrate one variant of our proposed systems is capable of separating new source tracks effortlessly.

Runtime verification or runtime monitoring equips safety-critical cyber-physical systems to augment design assurance measures and ensure operational safety and security. Cyber-physical systems have interaction failures, attack surfaces, and attack vectors resulting in unanticipated hazards and loss scenarios. These interaction failures pose challenges to runtime verification regarding monitoring specifications and monitoring placements for in-time detection of hazards. We develop a well-formed workflow model that connects system theoretic process analysis, commonly referred to as STPA, hazard causation information to lower-level runtime monitoring to detect hazards at the operational phase. Specifically, our model follows the DepDevOps paradigm to provide evidence and insights to runtime monitoring on what to monitor, where to monitor, and the monitoring context. We demonstrate and evaluate the value of multilevel monitors by injecting hazards on an autonomous emergency braking system model.

We consider statistical models arising from the common set of solutions to a sparse polynomial system with general coefficients. The maximum likelihood degree counts the number of critical points of the likelihood function restricted to the model. We prove the maximum likelihood degree of a sparse polynomial system is determined by its Newton polytopes and equals the mixed volume of a related Lagrange system of equations.

The adoption of Unmanned Aerial Vehicles (UAVs) for public safety applications has skyrocketed in the last years. Leveraging on Physical Random Access Channel (PRACH) preambles, in this paper we pioneer a novel localization technique for UAVs equipped with cellular base stations used in emergency scenarios. We exploit the new concept of Orthogonal Time Frequency Space (OTFS) modulation (tolerant to channel Doppler spread caused by UAVs motion) to build a fully standards-compliant OTFS-modulated PRACH transmission and reception scheme able to perform time-of-arrival (ToA) measurements. First, we analyze such novel ToA ranging technique, both analytically and numerically, to accurately and iteratively derive the distance between localized users and the points traversed by the UAV along its trajectory. Then, we determine the optimal UAV speed as a trade-off between the accuracy of the ranging technique and the power needed by the UAV to reach and keep its speed during emergency operations. Finally, we demonstrate that our solution outperforms standard PRACH-based localization techniques in terms of Root Mean Square Error (RMSE) by about 20% in quasi-static conditions and up to 80% in high-mobility conditions.

The minimum energy path (MEP) describes the mechanism of reaction, and the energy barrier along the path can be used to calculate the reaction rate in thermal systems. The nudged elastic band (NEB) method is one of the most commonly used schemes to compute MEPs numerically. It approximates an MEP by a discrete set of configuration images, where the discretization size determines both computational cost and accuracy of the simulations. In this paper, we consider a discrete MEP to be a stationary state of the NEB method and prove an optimal convergence rate of the discrete MEP with respect to the number of images. Numerical simulations for the transitions of some several proto-typical model systems are performed to support the theory.

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are exceptional and standard eigenvalue solvers, such as the QZ algorithm, tend to yield good accuracy despite the inevitable presence of roundoff error. Recently, Lotz and Noferini quantified this phenomenon by introducing the concept of $\delta$-weak eigenvalue condition numbers. In this work, we consider singular quadratic eigenvalue problems and two popular linearizations. Our results show that a correctly chosen linearization increases $\delta$-weak eigenvalue condition numbers only marginally, justifying the use of these linearizations in numerical solvers also in the singular case. We propose a very simple but often effective algorithm for computing well-conditioned eigenvalues of a singular quadratic eigenvalue problems by adding small random perturbations to the coefficients. We prove that the eigenvalue condition number is, with high probability, a reliable criterion for detecting and excluding spurious eigenvalues created from the singular part.

Training self-driving systems to be robust to the long-tail of driving scenarios is a critical problem. Model-based approaches leverage simulation to emulate a wide range of scenarios without putting users at risk in the real world. One promising path to faithful simulation is to train a forward model of the world to predict the future states of both the environment and the ego-vehicle given past states and a sequence of actions. In this paper, we argue that it is beneficial to model the state of the ego-vehicle, which often has simple, predictable and deterministic behavior, separately from the rest of the environment, which is much more complex and highly multimodal. We propose to model the ego-vehicle using a simple and differentiable kinematic model, while training a stochastic convolutional forward model on raster representations of the state to predict the behavior of the rest of the environment. We explore several configurations of such decoupled models, and evaluate their performance both with Model Predictive Control (MPC) and direct policy learning. We test our methods on the task of highway driving and demonstrate lower crash rates and better stability. The code is available at //github.com/vladisai/pytorch-PPUU/tree/ICLR2022.

We recall some of the history of the information-theoretic approach to deriving core results in probability theory and indicate parts of the recent resurgence of interest in this area with current progress along several interesting directions. Then we give a new information-theoretic proof of a finite version of de Finetti's classical representation theorem for finite-valued random variables. We derive an upper bound on the relative entropy between the distribution of the first $k$ in a sequence of $n$ exchangeable random variables, and an appropriate mixture over product distributions. The mixing measure is characterised as the law of the empirical measure of the original sequence, and de Finetti's result is recovered as a corollary. The proof is nicely motivated by the Gibbs conditioning principle in connection with statistical mechanics, and it follows along an appealing sequence of steps. The technical estimates required for these steps are obtained via the use of a collection of combinatorial tools known within information theory as `the method of types.'

Proactive dialogue system is able to lead the conversation to a goal topic and has advantaged potential in bargain, persuasion and negotiation. Current corpus-based learning manner limits its practical application in real-world scenarios. To this end, we contribute to advance the study of the proactive dialogue policy to a more natural and challenging setting, i.e., interacting dynamically with users. Further, we call attention to the non-cooperative user behavior -- the user talks about off-path topics when he/she is not satisfied with the previous topics introduced by the agent. We argue that the targets of reaching the goal topic quickly and maintaining a high user satisfaction are not always converge, because the topics close to the goal and the topics user preferred may not be the same. Towards this issue, we propose a new solution named I-Pro that can learn Proactive policy in the Interactive setting. Specifically, we learn the trade-off via a learned goal weight, which consists of four factors (dialogue turn, goal completion difficulty, user satisfaction estimation, and cooperative degree). The experimental results demonstrate I-Pro significantly outperforms baselines in terms of effectiveness and interpretability.