On the Convergence of Adam and Adagrad

We provide a simple proof of the convergence of the optimization algorithms Adam and Adagrad with the assumptions of smooth gradients and almost sure uniform bound on the $\ell_\infty$ norm of the gradients. This work builds on the techniques introduced by Ward et al. (2019) and extends them to the Adam optimizer. We show that in expectation, the squared norm of the objective gradient averaged over the trajectory has an upper-bound which is explicit in the constants of the problem, parameters of the optimizer and the total number of iterations N. This bound can be made arbitrarily small. In particular, Adam with a learning rate $\alpha=1/\sqrt{N}$ and a momentum parameter on squared gradients $\beta_2=1 - 1/N$ achieves the same rate of convergence $O(\ln(N)/\sqrt{N})$ as Adagrad. Thus, it is possible to use Adam as a finite horizon version of Adagrad, much like constant step size SGD can be used instead of its asymptotically converging decaying step size version.

Music Source Separation in the Waveform Domain

Source separation for music is the task of isolating contributions, or stems, from different instruments recorded individually and arranged together to form a song. Such components include voice, bass, drums and any other accompaniments. Contrarily to many audio synthesis tasks where the best performances are achieved by models that directly generate the waveform, the state-of-the-art in source separation for music is to compute masks on the magnitude spectrum. In this paper, we first show that an adaptation of Conv-Tasnet (Luo \& Mesgarani, 2019), a waveform-to-waveform model for source separation for speech, significantly beats the state-of-the-art on the MusDB dataset, the standard benchmark of multi-instrument source separation. Second, we observe that Conv-Tasnet follows a masking approach on the input signal, which has the potential drawback of removing parts of the relevant source without the capacity to reconstruct it. We propose Demucs, a new waveform-to-waveform model, which has an architecture closer to models for audio generation with more capacity on the decoder. Experiments on the MusDB dataset show that Demucs beats previously reported results in terms of signal to distortion ratio (SDR), but lower than Conv-Tasnet. Human evaluations show that Demucs has significantly higher quality (as assessed by mean opinion score) than Conv-Tasnet, but slightly more contamination from other sources, which explains the difference in SDR. Additional experiments with a larger dataset suggest that the gap in SDR between Demucs and Conv-Tasnet shrinks, showing that our approach is promising.

A Structured Prediction Approach for Generalization in Cooperative Multi-Agent Reinforcement Learning

Effective coordination is crucial to solve multi-agent collaborative (MAC) problems. While centralized reinforcement learning methods can optimally solve small MAC instances, they do not scale to large problems and they fail to generalize to scenarios different from those seen during training. In this paper, we consider MAC problems with some intrinsic notion of locality (e.g., geographic proximity) such that interactions between agents and tasks are locally limited. By leveraging this property, we introduce a novel structured prediction approach to assign agents to tasks. At each step, the assignment is obtained by solving a centralized optimization problem (the inference procedure) whose objective function is parameterized by a learned scoring model. We propose different combinations of inference procedures and scoring models able to represent coordination patterns of increasing complexity. The resulting assignment policy can be efficiently learned on small problem instances and readily reused in problems with more agents and tasks (i.e., zero-shot generalization). We report experimental results on a toy search and rescue problem and on several target selection scenarios in StarCraft: Brood War, in which our model significantly outperforms strong rule-based baselines on instances with 5 times more agents and tasks than those seen during training.

Demucs: Deep Extractor for Music Sources with extra unlabeled data remixed

We study the problem of source separation for music using deep learning with four known sources: drums, bass, vocals and other accompaniments. State-of-the-art approaches predict soft masks over mixture spectrograms while methods working on the waveform are lagging behind as measured on the standard MusDB benchmark. Our contribution is two fold. (i) We introduce a simple convolutional and recurrent model that outperforms the state-of-the-art model on waveforms, that is, Wave-U-Net, by 1.6 points of SDR (signal to distortion ratio). (ii) We propose a new scheme to leverage unlabeled music. We train a first model to extract parts with at least one source silent in unlabeled tracks, for instance without bass. We remix this extract with a bass line taken from the supervised dataset to form a new weakly supervised training example. Combining our architecture and scheme, we show that waveform methods can play in the same ballpark as spectrogram ones.

Growing Action Spaces

In complex tasks, such as those with large combinatorial action spaces, random exploration may be too inefficient to achieve meaningful learning progress. In this work, we use a curriculum of progressively growing action spaces to accelerate learning. We assume the environment is out of our control, but that the agent may set an internal curriculum by initially restricting its action space. Our approach uses off-policy reinforcement learning to estimate optimal value functions for multiple action spaces simultaneously and efficiently transfers data, value estimates, and state representations from restricted action spaces to the full task. We show the efficacy of our approach in proof-of-concept control tasks and on challenging large-scale StarCraft micromanagement tasks with large, multi-agent action spaces.

Fully Convolutional Speech Recognition

Current state-of-the-art speech recognition systems build on recurrent neural networks for acoustic and/or language modeling, and rely on feature extraction pipelines to extract mel-filterbanks or cepstral coefficients. In this paper we present an alternative approach based solely on convolutional neural networks, leveraging recent advances in acoustic models from the raw waveform and language modeling. This fully convolutional approach is trained end-to-end to predict characters from the raw waveform, removing the feature extraction step altogether. An external convolutional language model is used to decode words. On Wall Street Journal, our model matches the current state-of-the-art. On Librispeech, we report state-of-the-art performance among end-to-end models, including Deep Speech 2 trained with 12 times more acoustic data and significantly more linguistic data.

To Reverse the Gradient or Not: An Empirical Comparison of Adversarial and Multi-task Learning in Speech Recognition

Transcribed datasets typically contain speaker identity for each instance in the data. We investigate two ways to incorporate this information during training: Multi-Task Learning and Adversarial Learning. In multi-task learning, the goal is speaker prediction; we expect a performance improvement with this joint training if the two tasks of speech recognition and speaker recognition share a common set of underlying features. In contrast, adversarial learning is a means to learn representations invariant to the speaker. We then expect better performance if this learnt invariance helps generalizing to new speakers. While the two approaches seem natural in the context of speech recognition, they are incompatible because they correspond to opposite gradients back-propagated to the model. In order to better understand the effect of these approaches in terms of error rates, we compare both strategies in controlled settings. Moreover, we explore the use of additional untranscribed data in a semi-supervised, adversarial learning manner to improve error rates. Our results show that deep models trained on big datasets already develop invariant representations to speakers without any auxiliary loss. When considering adversarial learning and multi-task learning, the impact on the acoustic model seems minor. However, models trained in a semi-supervised manner can improve error-rates.

Forward Modeling for Partial Observation Strategy Games - A StarCraft Defogger

We formulate the problem of defogging as state estimation and future state prediction from previous, partial observations in the context of real-time strategy games. We propose to employ encoder-decoder neural networks for this task, and introduce proxy tasks and baselines for evaluation to assess their ability of capturing basic game rules and high-level dynamics. By combining convolutional neural networks and recurrent networks, we exploit spatial and sequential correlations and train well-performing models on a large dataset of human games of StarCraft: Brood War. Finally, we demonstrate the relevance of our models to downstream tasks by applying them for enemy unit prediction in a state-of-the-art, rule-based StarCraft bot. We observe improvements in win rates against several strong community bots.

High-Level Strategy Selection under Partial Observability in StarCraft: Brood War

We consider the problem of high-level strategy selection in the adversarial setting of real-time strategy games from a reinforcement learning perspective, where taking an action corresponds to switching to the respective strategy. Here, a good strategy successfully counters the opponent's current and possible future strategies which can only be estimated using partial observations. We investigate whether we can utilize the full game state information during training time (in the form of an auxiliary prediction task) to increase performance. Experiments carried out within a StarCraft: Brood War bot against strong community bots show substantial win rate improvements over a fixed-strategy baseline and encouraging results when learning with the auxiliary task.

SING: Symbol-to-Instrument Neural Generator

Recent progress in deep learning for audio synthesis opens the way to models that directly produce the waveform, shifting away from the traditional paradigm of relying on vocoders or MIDI synthesizers for speech or music generation. Despite their successes, current state-of-the-art neural audio synthesizers such as WaveNet and SampleRNN suffer from prohibitive training and inference times because they are based on autoregressive models that generate audio samples one at a time at a rate of 16kHz. In this work, we study the more computationally efficient alternative of generating the waveform frame-by-frame with large strides. We present SING, a lightweight neural audio synthesizer for the original task of generating musical notes given desired instrument, pitch and velocity. Our model is trained end-to-end to generate notes from nearly 1000 instruments with a single decoder, thanks to a new loss function that minimizes the distances between the log spectrograms of the generated and target waveforms. On the generalization task of synthesizing notes for pairs of pitch and instrument not seen during training, SING produces audio with significantly improved perceptual quality compared to a state-of-the-art autoencoder based on WaveNet as measured by a Mean Opinion Score (MOS), and is about 32 times faster for training and 2, 500 times faster for inference.