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In Imitation Learning (IL), utilizing suboptimal and heterogeneous demonstrations presents a substantial challenge due to the varied nature of real-world data. However, standard IL algorithms consider these datasets as homogeneous, thereby inheriting the deficiencies of suboptimal demonstrators. Previous approaches to this issue typically rely on impractical assumptions like high-quality data subsets, confidence rankings, or explicit environmental knowledge. This paper introduces IRLEED, Inverse Reinforcement Learning by Estimating Expertise of Demonstrators, a novel framework that overcomes these hurdles without prior knowledge of demonstrator expertise. IRLEED enhances existing Inverse Reinforcement Learning (IRL) algorithms by combining a general model for demonstrator suboptimality to address reward bias and action variance, with a Maximum Entropy IRL framework to efficiently derive the optimal policy from diverse, suboptimal demonstrations. Experiments in both online and offline IL settings, with simulated and human-generated data, demonstrate IRLEED's adaptability and effectiveness, making it a versatile solution for learning from suboptimal demonstrations., Comment: 12 pages, 3 figures, preprint

In this paper we study the pickup and delivery problem with multiple transportation modalities, and address the challenge of efficiently allocating transportation resources while price matching users with their desired delivery modes. Precisely, we consider that orders are demanded by a heterogeneous population of users with varying trade-offs between price and latency. To capture how prices affect the behavior of heterogeneous selfish users choosing between multiple delivery modes, we construct a congestion game taking place over a star network with independent sub-networks composed of parallel links connecting users with their preferred delivery method. Using the unique geometry of this network we prove that one can define prices explicitly to induce any desired network flow, i.e, given a desired allocation strategy we have a closed-form solution for the delivery prices. In connection with prior works that consider non-atomic congestion games, our result shows that one can simplify the Linear Program formulations used to solve for edge prices by first finding the path prices combinatorially. We conclude by performing a case study on a meal delivery problem with multiple courier modalities using data from real world instances., Comment: 8 pages, 2 figures

We derive a covariance formula for the number of excursion or level set components of a smooth stationary Gaussian field on $\mathbb{R}^d$ contained in compact domains. We also present two applications of this formula: (1) for fields whose correlations are integrable we prove that the variance of the component count in large domains is of volume order and give an expression for the leading constant, and (2) for fields with slower decay of correlation we give an upper bound on the variance which is of optimal order if correlations are regularly varying, and improves on best-known bounds if correlations are oscillating (e.g.\ monochromatic random waves).

We prove convergence of Hausdorff measure of level sets of smooth Gaussian fields when the levels converge. Given two coupled stationary fields $f_1, f_2$ , we estimate the difference of Hausdorff measure of level sets in expectation, in terms of $C^2$-fluctuations of the field $F=f_1-f_2$. The main idea in the proof is to represent difference in volume as an integral of mean curvature using the divergence theorem. This approach is different from using Kac-Rice type formula as main tool in the analysis., Comment: 9 pages

In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their (conjectured) connection to the percolation theory.

For a smooth stationary Gaussian field on $\mathbb{R}^d$ and level $\ell \in \mathbb{R}$, we consider the number of connected components of the excursion set $\{f \ge \ell\}$ (or level set $\{f = \ell\}$) contained in large domains. The mean of this quantity is known to scale like the volume of the domain under general assumptions on the field. We prove that, assuming sufficient decay of correlations (e.g. the Bargmann-Fock field), a central limit theorem holds with volume-order scaling. Previously such a result had only been established for `additive' geometric functionals of the excursion/level sets (e.g. the volume or Euler characteristic) using Hermite expansions. Our approach, based on a martingale analysis, is more robust and can be generalised to a wider class of topological functionals. A major ingredient in the proof is a third moment bound on critical points, which is of independent interest., Comment: 33 pages, 1 figure

Many existing imitation learning datasets are collected from multiple demonstrators, each with different expertise at different parts of the environment. Yet, standard imitation learning algorithms typically treat all demonstrators as homogeneous, regardless of their expertise, absorbing the weaknesses of any suboptimal demonstrators. In this work, we show that unsupervised learning over demonstrator expertise can lead to a consistent boost in the performance of imitation learning algorithms. We develop and optimize a joint model over a learned policy and expertise levels of the demonstrators. This enables our model to learn from the optimal behavior and filter out the suboptimal behavior of each demonstrator. Our model learns a single policy that can outperform even the best demonstrator, and can be used to estimate the expertise of any demonstrator at any state. We illustrate our findings on real-robotic continuous control tasks from Robomimic and discrete environments such as MiniGrid and chess, out-performing competing methods in $21$ out of $23$ settings, with an average of $7\%$ and up to $60\%$ improvement in terms of the final reward., Comment: ICML 2022. 17 pages, 4 figures

In the past two decades we have seen the popularity of neural networks increase in conjunction with their classification accuracy. Parallel to this, we have also witnessed how fragile the very same prediction models are: tiny perturbations to the inputs can cause misclassification errors throughout entire datasets. In this paper, we consider perturbations bounded by the $\ell_0$--norm, which have been shown as effective attacks in the domains of image-recognition, natural language processing, and malware-detection. To this end, we propose a novel defense method that consists of "truncation" and "adversarial training". We then theoretically study the Gaussian mixture setting and prove the asymptotic optimality of our proposed classifier. Motivated by the insights we obtain, we extend these components to neural network classifiers. We conduct numerical experiments in the domain of computer vision using the MNIST and CIFAR datasets, demonstrating significant improvement for the robust classification error of neural networks.

This paper describes Mixer-TTS, a non-autoregressive model for mel-spectrogram generation. The model is based on the MLP-Mixer architecture adapted for speech synthesis. The basic Mixer-TTS contains pitch and duration predictors, with the latter being trained with an unsupervised TTS alignment framework. Alongside the basic model, we propose the extended version which additionally uses token embeddings from a pre-trained language model. Basic Mixer-TTS and its extended version achieve a mean opinion score (MOS) of 4.05 and 4.11, respectively, compared to a MOS of 4.27 of original LJSpeech samples. Both versions have a small number of parameters and enable much faster speech synthesis compared to the models with similar quality., Comment: Preprint. Submitted to ICASSP-22

Coordination is often critical to forming prosocial behaviors -- behaviors that increase the overall sum of rewards received by all agents in a multi-agent game. However, state of the art reinforcement learning algorithms often suffer from converging to socially less desirable equilibria when multiple equilibria exist. Previous works address this challenge with explicit reward shaping, which requires the strong assumption that agents can be forced to be prosocial. We propose using a less restrictive peer-rewarding mechanism, gifting, that guides the agents toward more socially desirable equilibria while allowing agents to remain selfish and decentralized. Gifting allows each agent to give some of their reward to other agents. We employ a theoretical framework that captures the benefit of gifting in converging to the prosocial equilibrium by characterizing the equilibria's basins of attraction in a dynamical system. With gifting, we demonstrate increased convergence of high risk, general-sum coordination games to the prosocial equilibrium both via numerical analysis and experiments., Comment: 9 pages, 6 figures, IJCAI 2021

We propose TalkNet, a non-autoregressive convolutional neural model for speech synthesis with explicit pitch and duration prediction. The model consists of three feed-forward convolutional networks. The first network predicts grapheme durations. An input text is expanded by repeating each symbol according to the predicted duration. The second network predicts pitch value for every mel frame. The third network generates a mel-spectrogram from the expanded text conditioned on predicted pitch. All networks are based on 1D depth-wise separable convolutional architecture. The explicit duration prediction eliminates word skipping and repeating. The quality of the generated speech nearly matches the best auto-regressive models - TalkNet trained on the LJSpeech dataset got MOS 4.08. The model has only 13.2M parameters, almost 2x less than the present state-of-the-art text-to-speech models. The non-autoregressive architecture allows for fast training and inference. The small model size and fast inference make the TalkNet an attractive candidate for embedded speech synthesis., Comment: arXiv admin note: substantial text overlap with arXiv:2005.05514

Bi-modal delivery systems are a promising solution to the challenges posed by the increasing demand of e-commerce. Due to the potential benefit drones can have on logistics networks such as delivery systems, some countries have taken steps towards integrating drones into their airspace. In this paper we aim to quantify this potential by developing a mathematical model for a Bi-modal delivery system composed of trucks and drones. We propose an optimization formulation that can be efficiently solved in order to design socially-optimal routing and allocation policies. We incorporate both societal cost in terms of road congestion and parcel delivery latency in our formulation. Our model is able to quantify the effect drones have on mitigating road congestion, and can solve for the path routing needed to minimize the chosen objective. To accurately capture the effect of stopping trucks on road latency, we model it using SUMO by simulating roads shared by trucks and cars. Based on this, we show that the proposed framework is computationally feasible to scale due to its reliance on convex quadratic optimization techniques., Comment: Published at the European Control Conference Proceedings 2022 (ECC-2022)

The COVID-19 pandemic has severely affected many aspects of people's daily lives. While many countries are in a re-opening stage, some effects of the pandemic on people's behaviors are expected to last much longer, including how they choose between different transport options. Experts predict considerably delayed recovery of the public transport options, as people try to avoid crowded places. In turn, significant increases in traffic congestion are expected, since people are likely to prefer using their own vehicles or taxis as opposed to riskier and more crowded options such as the railway. In this paper, we propose to use financial incentives to set the tradeoff between risk of infection and congestion to achieve safe and efficient transportation networks. To this end, we formulate a network optimization problem to optimize taxi fares. For our framework to be useful in various cities and times of the day without much designer effort, we also propose a data-driven approach to learn human preferences about transport options, which is then used in our taxi fare optimization. Our user studies and simulation experiments show our framework is able to minimize congestion and risk of infection., Comment: ICCPS 2021. 11 pages, 4 figures

We propose a neural network for zero-shot voice conversion (VC) without any parallel or transcribed data. Our approach uses pre-trained models for automatic speech recognition (ASR) and speaker embedding, obtained from a speaker verification task. Our model is fully convolutional and non-autoregressive except for a small pre-trained recurrent neural network for speaker encoding. ConVoice can convert speech of any length without compromising quality due to its convolutional architecture. Our model has comparable quality to similar state-of-the-art models while being extremely fast.

We propose TalkNet, a convolutional non-autoregressive neural model for speech synthesis. The model consists of two feed-forward convolutional networks. The first network predicts grapheme durations. An input text is expanded by repeating each symbol according to the predicted duration. The second network generates a mel-spectrogram from the expanded text. To train a grapheme duration predictor, we add the grapheme duration to the training dataset using a pre-trained Connectionist Temporal Classification (CTC)-based speech recognition model. The explicit duration prediction eliminates word skipping and repeating. Experiments on the LJSpeech dataset show that the speech quality nearly matches auto-regressive models. The model is very compact -- it has 10.8M parameters, almost 3x less than the present state-of-the-art text-to-speech models. The non-autoregressive architecture allows for fast training and inference.

We consider a family of Bessel Processes that depend on the starting point $x$ and dimension $\delta$, but are driven by the same Brownian motion. Our main result is that almost surely the first time a process hits $0$ is jointly continuous in $x$ and $\delta$, provided $\delta\le 0$. As an application, we show that the SLE($\kappa$) welding homeomorphism is continuous in $\kappa$ for $\kappa\in [0,4]$. Our motivation behind this is to study the well known problem of the continuity of SLE$_\kappa$ in $\kappa$. The main tool in our proofs is random walks with increments distributed as infinite mean Inverse-Gamma laws., Comment: 12 pages

Questions regarding the continuity in $\kappa$ of the $SLE_{\kappa}$ traces and maps appear very naturally in the study of SLE. In order to study the first question, we consider a natural coupling of SLE traces: for different values of $\kappa$ we use the same Brownian motion. It is very natural to assume that with probability one, $SLE_\kappa$ depends continuously on $\kappa$. It is rather easy to show that $SLE$ is continuous in the Carath\'eodory sense, but showing that $SLE$ traces are continuous in the uniform sense is much harder. In this note we show that for a given sequence $\kappa_j\to\kappa \in (0, 8/3)$, for almost every Brownian motion $SLE_\kappa$ traces converge locally uniformly. This result was also recently obtained by Friz, Tran and Yuan using different methods. In our analysis, we provide a constructive way to study the $SLE_{\kappa}$ traces for varying parameter $\kappa \in (0, 8/3)$. The argument is based on a new dynamical view on the approximation of SLE curves by curves driven by a piecewise square root approximation of the Brownian motion. The second question can be answered naturally in the framework of Rough Path Theory. Using this theory, we prove that the solutions of the backward Loewner Differential Equation driven by $\sqrt{\kappa}B_t$ when started away from the origin are continuous in the $p$-variation topology in the parameter $\kappa$, for all $\kappa \in \mathbb{R}_+$, Comment: 22 pages, no figures

It is well know that $SLE_\kappa$ curves exhibit a phase transition at $\kappa=4$. For $\kappa\le 4$ they are simple curves with probability one, for $\kappa>4$ they are not. The standard proof is based on the analysis of the Bessel SDE of dimension $d=1+4/\kappa$. We propose a different approach which is based on the analysis of the Bessel SDE with $d=1-4/\kappa$. This not only gives a new perspective, but also allows to describe the formation of the SLE `bubbles' for $\kappa>4$., Comment: 14 pages, no figures

In this paper we obtain a range of quantitative results of the following type: given two centered Gaussian fields with close covariance kernels we construct a coupling such that the fields are uniformly close on some compact with probability very close to one. As an application, we show that it is possible to couple arithmetic random waves so that they converge locally uniformly to the random plane wave and estimate the rate of convergence.

We study the behaviour of the point process of critical points of isotropic stationary Gaussian fields. We compute the main term in the asymptotic expansion of the two-point correlation function near the diagonal. Our main result implies that for a 'generic' field the critical points neither repel nor attract each other. Our analysis also allows to study how the short-range behaviour of critical points depends on their index., Comment: This version of the paper contains the text of the paper accepted for publication in 'Electronic Communications in Probability' and three appendices which show some technical computations. arXiv admin note: text overlap with arXiv:1704.04943

We propose a new end-to-end neural acoustic model for automatic speech recognition. The model is composed of multiple blocks with residual connections between them. Each block consists of one or more modules with 1D time-channel separable convolutional layers, batch normalization, and ReLU layers. It is trained with CTC loss. The proposed network achieves near state-of-the-art accuracy on LibriSpeech and Wall Street Journal, while having fewer parameters than all competing models. We also demonstrate that this model can be effectively fine-tuned on new datasets., Comment: Submitted to ICASSP 2020

NeMo (Neural Modules) is a Python framework-agnostic toolkit for creating AI applications through re-usability, abstraction, and composition. NeMo is built around neural modules, conceptual blocks of neural networks that take typed inputs and produce typed outputs. Such modules typically represent data layers, encoders, decoders, language models, loss functions, or methods of combining activations. NeMo makes it easy to combine and re-use these building blocks while providing a level of semantic correctness checking via its neural type system. The toolkit comes with extendable collections of pre-built modules for automatic speech recognition and natural language processing. Furthermore, NeMo provides built-in support for distributed training and mixed precision on latest NVIDIA GPUs. NeMo is open-source https://github.com/NVIDIA/NeMo, Comment: 6 pages plus references

For a smooth, stationary, planar Gaussian field, we consider the number of connected components of its excursion set (or level set) contained in a large square of area $R^2$. The mean number of components is known to be of order $R^2$ for generic fields and all levels. We show that for certain fields with positive spectral density near the origin (including the Bargmann-Fock field), and for certain levels $\ell$, these random variables have fluctuations of order at least $R$, and hence variance of order at least $R^2$. In particular, this holds for excursion sets when $\ell$ is in some neighbourhood of zero, and it holds for excursion/level sets when $\ell$ is sufficiently large. We prove stronger fluctuation lower bounds of order $R^\alpha$, $\alpha \in [1,2]$, in the case that the spectral density has a singularity at the origin. Finally, we show that the number of excursion/level sets for the Random Plane Wave at certain levels has fluctuations of order at least $R^{3/2}$, and hence variance of order at least~$R^3$. We expect that these bounds are of the correct order, at least for generic levels., Comment: 38 pages, 2 figures

In this paper we study the nodal lines of random eigenfunctions of the Laplacian on the torus, the so called 'arithmetic waves'. To be more precise, we study the number of intersections of the nodal line with a straight interval in a given direction. We are interested in how this number depends on the length and direction of the interval and the distribution of spectral measure of the random wave. We analyse the second factorial moment in the short interval regime and the persistence probability in the long interval regime. We also study relations between the Cilleruelo and Cilleruelo-type fields. We give an explicit coupling between these fields which on mesoscopic scales preserves the structure of the nodal sets with probability close to one.

Nazarov and Sodin have shown that the number of connected components of the nodal set of a planar Gaussian field in a ball of radius $R$, normalised by area, converges to a constant as $R\to \infty $. This has been generalised to excursion/level sets at arbitrary levels, implying the existence of functionals $c_{ES}(\ell )$ and $c_{LS}(\ell )$ that encode the density of excursion/level set components at the level $\ell $. We prove that these functionals are continuously differentiable for a wide class of fields. This follows from a more general result, which derives differentiability of the functionals from the decay of the probability of `four-arm events' for the field conditioned to have a saddle point at the origin. For some fields, including the important special cases of the Random Plane Wave and the Bargmann-Fock field, we also derive stochastic monotonicity of the conditioned field, which allows us to deduce regions on which $c_{ES}(\ell )$ and $c_{LS}(\ell )$ are monotone., Comment: 39 pages, 8 figures. Updated to match published version

We study in depth the nesting graph and volume distribution of the nodal domains of a Gaussian field, which have been shown in previous works to exhibit asymptotic laws. A striking link is established between the asymptotic mean connectivity of a nodal domain (i.e.\ the vertex degree in its nesting graph) and the positivity of the percolation probability of the field, along with a direct dependence of the average nodal volume on the percolation probability. Our results support the prevailing ansatz that the mean connectivity and volume of a nodal domain is conserved for generic random fields in dimension $d=2$ but not in $d \ge 3$, and are applied to a number of concrete motivating examples., Comment: 29 pages, 4 figures

We derive a covariance formula for the class of `topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of the field, for example (i) crossing events for level or excursion sets, (ii) events measurable with respect to the number of connected components of level or excursion sets of a given diffeomorphism class, and (iii) persistence events. As an application of the covariance formula, we derive strong mixing bounds for topological events, as well as lower concentration inequalities for additive topological functionals (e.g. the number of connected components) of the level sets that satisfy a law of large numbers. The covariance formula also gives an alternate justification of the Harris criterion, which conjecturally describes the boundary of the percolation university class for level sets of stationary Gaussian fields. Our work is inspired by a recent paper by Rivera and Vanneuville, in which a correlation inequality was derived for certain topological events on the plane, as well as by an old result of Piterbarg, in which a similar covariance formula was established for finite-dimensional Gaussian vectors., Comment: 46 pages, 3 figures. Version accepted for publication in Annals of Probability