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We introduce a novel approach to options trading strategies using a highly scalable and data-driven machine learning algorithm. In contrast to traditional approaches that often require specifications of underlying market dynamics or assumptions on an option pricing model, our models depart fundamentally from the need for these prerequisites, directly learning non-trivial mappings from market data to optimal trading signals. Backtesting on more than a decade of option contracts for equities listed on the S&P 100, we demonstrate that deep learning models trained according to our end-to-end approach exhibit significant improvements in risk-adjusted performance over existing rules-based trading strategies. We find that incorporating turnover regularization into the models leads to further performance enhancements at prohibitively high levels of transaction costs.

We present an energy/entropy stable and high order accurate finite difference method for solving the nonlinear (rotating) shallow water equations (SWE) in vector invariant form using the newly developed dual-pairing and dispersion-relation preserving summation-by-parts finite difference operators. We derive new well-posed boundary conditions for the SWE in one space dimension, formulated in terms of fluxes and applicable to linear and nonlinear SWEs. For the nonlinear SWE, entropy stability ensures the boundedness of numerical solution but does not guarantee convergence. Adequate amount of numerical dissipation is necessary to control high frequency errors which could negatively impact accuracy in the numerical simulations. Using the dual-pairing summation by parts framework, we derive high order accurate and nonlinear hyper-viscosity operator which dissipates entropy and enstrophy. The hyper-viscosity operator effectively minimises oscillations from shocks and discontinuities, and eliminates high frequency grid-scale errors. The numerical method is most suitable for the simulations of subcritical flows typically observed in atmospheric and geostrophic flow problems. We prove a priori error estimates for the semi-discrete approximations of both linear and nonlinear SWE. Convergence, accuracy, and well-balanced properties are verified via the method of manufactured solutions and canonical test problems such as the dam break and lake at rest. Numerical simulations in two-dimensions are presented which include the rotating and merging vortex problem and barotropic shear instability, with fully developed turbulence., Comment: 37 pages, 14 figures, comments are welcome

Forecasting models for systematic trading strategies do not adapt quickly when financial market conditions rapidly change, as was seen in the advent of the COVID-19 pandemic in 2020, causing many forecasting models to take loss-making positions. To deal with such situations, we propose a novel time-series trend-following forecaster that can quickly adapt to new market conditions, referred to as regimes. We leverage recent developments from the deep learning community and use few-shot learning. We propose the Cross Attentive Time-Series Trend Network -- X-Trend -- which takes positions attending over a context set of financial time-series regimes. X-Trend transfers trends from similar patterns in the context set to make forecasts, then subsequently takes positions for a new distinct target regime. By quickly adapting to new financial regimes, X-Trend increases Sharpe ratio by 18.9% over a neural forecaster and 10-fold over a conventional Time-series Momentum strategy during the turbulent market period from 2018 to 2023. Our strategy recovers twice as quickly from the COVID-19 drawdown compared to the neural-forecaster. X-Trend can also take zero-shot positions on novel unseen financial assets obtaining a 5-fold Sharpe ratio increase versus a neural time-series trend forecaster over the same period. Furthermore, the cross-attention mechanism allows us to interpret the relationship between forecasts and patterns in the context set., Comment: minor edits

This paper examines the asymptotic convergence properties of Lipschitz interpolation methods within the context of bounded stochastic noise. In the first part of the paper, we establish probabilistic consistency guarantees of the classical approach in a general setting and derive upper bounds on the uniform convergence rates. These bounds align with well-established optimal rates of non-parametric regression obtained in related settings and provide new precise upper bounds on the non-parametric regression problem under bounded noise assumptions. Practically, they can serve as a theoretical tool for comparing Lipschitz interpolation to alternative non-parametric regression methods, providing a condition on the behaviour of the noise at the boundary of its support which indicates when Lipschitz interpolation should be expected to asymptotically outperform or underperform other approaches. In the second part, we expand upon these results to include asymptotic guarantees for online learning of dynamics in discrete-time stochastic systems and illustrate their utility in deriving closed-loop stability guarantees of a simple controller. We also explore applications where the main assumption of prior knowledge of the Lipschitz constant is removed by adopting the LACKI framework (Calliess et al. (2020)) and deriving general asymptotic consistency., Comment: Preprint

We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial boundary value problem is well-posed. A finite volume method is developed based on the summation-by-parts framework with the boundary conditions implemented weakly using penalties. Stability is proven by deriving a discrete energy estimate analogous to the continuous estimate. The continuous and discrete analysis covers all flow regimes. Numerical experiments are presented verifying the analysis., Comment: 23 pages, 4 figures

We consider a conditional factor model for a multivariate portfolio of United States equities in the context of analysing a statistical arbitrage trading strategy. A state space framework underlies the factor model whereby asset returns are assumed to be a noisy observation of a linear combination of factor values and latent factor risk premia. Filter and state prediction estimates for the risk premia are retrieved in an online way. Such estimates induce filtered asset returns that can be compared to measurement observations, with large deviations representing candidate mean reversion trades. Further, in that the risk premia are modelled as time-varying quantities, non-stationarity in returns is de facto captured. We study an empirical trading strategy respectful of transaction costs, and demonstrate performance over a long history of 29 years, for both a linear and a non-linear state space model. Our results show that the model is competitive relative to the results of other methods, including simple benchmarks and other cutting-edge approaches as published in the literature. Also of note, while strategy performance degradation is noticed through time -- especially for the most recent years -- the strategy continues to offer compelling economics, and has scope for further advancement.

Network momentum provides a novel type of risk premium, which exploits the interconnections among assets in a financial network to predict future returns. However, the current process of constructing financial networks relies heavily on expensive databases and financial expertise, limiting accessibility for small-sized and academic institutions. Furthermore, the traditional approach treats network construction and portfolio optimisation as separate tasks, potentially hindering optimal portfolio performance. To address these challenges, we propose L2GMOM, an end-to-end machine learning framework that simultaneously learns financial networks and optimises trading signals for network momentum strategies. The model of L2GMOM is a neural network with a highly interpretable forward propagation architecture, which is derived from algorithm unrolling. The L2GMOM is flexible and can be trained with diverse loss functions for portfolio performance, e.g. the negative Sharpe ratio. Backtesting on 64 continuous future contracts demonstrates a significant improvement in portfolio profitability and risk control, with a Sharpe ratio of 1.74 across a 20-year period., Comment: 9 pages

We investigate the concept of network momentum, a novel trading signal derived from momentum spillover across assets. Initially observed within the confines of pairwise economic and fundamental ties, such as the stock-bond connection of the same company and stocks linked through supply-demand chains, momentum spillover implies a propagation of momentum risk premium from one asset to another. The similarity of momentum risk premium, exemplified by co-movement patterns, has been spotted across multiple asset classes including commodities, equities, bonds and currencies. However, studying the network effect of momentum spillover across these classes has been challenging due to a lack of readily available common characteristics or economic ties beyond the company level. In this paper, we explore the interconnections of momentum features across a diverse range of 64 continuous future contracts spanning these four classes. We utilise a linear and interpretable graph learning model with minimal assumptions to reveal the intricacies of the momentum spillover network. By leveraging the learned networks, we construct a network momentum strategy that exhibits a Sharpe ratio of 1.5 and an annual return of 22%, after volatility scaling, from 2000 to 2022. This paper pioneers the examination of momentum spillover across multiple asset classes using only pricing data, presents a multi-asset investment strategy based on network momentum, and underscores the effectiveness of this strategy through robust empirical analysis., Comment: 27 pages

Modern neural networks are undeniably successful. Numerous works study how the curvature of loss landscapes can affect the quality of solutions. In this work we study the loss landscape by considering the Hessian matrix during network training with large learning rates - an attractive regime that is (in)famously unstable. We characterise the instabilities of gradient descent, and we observe the striking phenomena of \textit{landscape flattening} and \textit{landscape shift}, both of which are intimately connected to the instabilities of training., Comment: arXiv admin note: text overlap with arXiv:2305.18490

We introduce Deep Inception Networks (DINs), a family of Deep Learning models that provide a general framework for end-to-end systematic trading strategies. DINs extract time series (TS) and cross sectional (CS) features directly from daily price returns. This removes the need for handcrafted features, and allows the model to learn from TS and CS information simultaneously. DINs benefit from a fully data-driven approach to feature extraction, whilst avoiding overfitting. Extending prior work on Deep Momentum Networks, DIN models directly output position sizes that optimise Sharpe ratio, but for the entire portfolio instead of individual assets. We propose a novel loss term to balance turnover regularisation against increased systemic risk from high correlation to the overall market. Using futures data, we show that DIN models outperform traditional TS and CS benchmarks, are robust to a range of transaction costs and perform consistently across random seeds. To balance the general nature of DIN models, we provide examples of how attention and Variable Selection Networks can aid the interpretability of investment decisions. These model-specific methods are particularly useful when the dimensionality of the input is high and variable importance fluctuates dynamically over time. Finally, we compare the performance of DIN models on other asset classes, and show how the space of potential features can be customised., Comment: 17 pages, 12 figures

We propose a new regularization scheme for the optimization of deep learning architectures, G-TRACER ("Geometric TRACE Ratio"), which promotes generalization by seeking flat minima, and has a sound theoretical basis as an approximation to a natural-gradient descent based optimization of a generalized Bayes objective. By augmenting the loss function with a TRACER, curvature-regularized optimizers (eg SGD-TRACER and Adam-TRACER) are simple to implement as modifications to existing optimizers and don't require extensive tuning. We show that the method converges to a neighborhood (depending on the regularization strength) of a local minimum of the unregularized objective, and demonstrate competitive performance on a number of benchmark computer vision and NLP datasets, with a particular focus on challenging low signal-to-noise ratio problems., Comment: 16 pages, 2 figures

Modern neural networks are undeniably successful. Numerous studies have investigated how the curvature of loss landscapes can affect the quality of solutions. In this work we consider the Hessian matrix during network training. We reiterate the connection between the number of "well-determined" or "effective" parameters and the generalisation performance of neural nets, and we demonstrate its use as a tool for model comparison. By considering the local curvature, we propose Sharpness Adjusted Number of Effective parameters (SANE), a measure of effective dimensionality for the quality of solutions. We show that SANE is robust to large learning rates, which represent learning regimes that are attractive but (in)famously unstable. We provide evidence and characterise the Hessian shifts across "loss basins" at large learning rates. Finally, extending our analysis to deeper neural networks, we provide an approximation to the full-network Hessian, exploiting the natural ordering of neural weights, and use this approximation to provide extensive empirical evidence for our claims.

We derive well-posed boundary conditions for the linearized Serre equations in one spatial dimension by utilizing the energy method. An energy stable and conservative discontinuous Galerkin spectral element method with simple upwind numerical fluxes is proposed for solving the initial boundary value problem. We derive discrete energy estimates for the numerical approximation and prove a priori error estimates in the energy norm. Detailed numerical examples are provided to verify the theoretical analysis and show convergence of numerical errors.

We introduce Spatio-Temporal Momentum strategies, a class of models that unify both time-series and cross-sectional momentum strategies by trading assets based on their cross-sectional momentum features over time. While both time-series and cross-sectional momentum strategies are designed to systematically capture momentum risk premia, these strategies are regarded as distinct implementations and do not consider the concurrent relationship and predictability between temporal and cross-sectional momentum features of different assets. We model spatio-temporal momentum with neural networks of varying complexities and demonstrate that a simple neural network with only a single fully connected layer learns to simultaneously generate trading signals for all assets in a portfolio by incorporating both their time-series and cross-sectional momentum features. Backtesting on portfolios of 46 actively-traded US equities and 12 equity index futures contracts, we demonstrate that the model is able to retain its performance over benchmarks in the presence of high transaction costs of up to 5-10 basis points. In particular, we find that the model when coupled with least absolute shrinkage and turnover regularization results in the best performance over various transaction cost scenarios.

The Black-Litterman model extends the framework of the Markowitz Modern Portfolio Theory to incorporate investor views. We consider a case where multiple view estimates, including uncertainties, are given for the same underlying subset of assets at a point in time. This motivates our consideration of data fusion techniques for combining information from multiple sources. In particular, we consider consistency-based methods that yield fused view and uncertainty pairs; such methods are not common to the quantitative finance literature. We show a relevant, modern case of incorporating machine learning model-derived view and uncertainty estimates, and the impact on portfolio allocation, with an example subsuming Arbitrage Pricing Theory. Hence we show the value of the Black-Litterman model in combination with information fusion and artificial intelligence-grounded prediction methods., Comment: 25 pages, 5 figures

Sequential Bayesian inference can be used for continual learning to prevent catastrophic forgetting of past tasks and provide an informative prior when learning new tasks. We revisit sequential Bayesian inference and test whether having access to the true posterior is guaranteed to prevent catastrophic forgetting in Bayesian neural networks. To do this we perform sequential Bayesian inference using Hamiltonian Monte Carlo. We propagate the posterior as a prior for new tasks by fitting a density estimator on Hamiltonian Monte Carlo samples. We find that this approach fails to prevent catastrophic forgetting demonstrating the difficulty in performing sequential Bayesian inference in neural networks. From there we study simple analytical examples of sequential Bayesian inference and CL and highlight the issue of model misspecification which can lead to sub-optimal continual learning performance despite exact inference. Furthermore, we discuss how task data imbalances can cause forgetting. From these limitations, we argue that we need probabilistic models of the continual learning generative process rather than relying on sequential Bayesian inference over Bayesian neural network weights. In this vein, we also propose a simple baseline called Prototypical Bayesian Continual Learning, which is competitive with state-of-the-art Bayesian continual learning methods on class incremental continual learning vision benchmarks., Comment: Published in Entropy, 24 pages, 14 figures

The UK COVID-19 Vocal Audio Dataset is designed for the training and evaluation of machine learning models that classify SARS-CoV-2 infection status or associated respiratory symptoms using vocal audio. The UK Health Security Agency recruited voluntary participants through the national Test and Trace programme and the REACT-1 survey in England from March 2021 to March 2022, during dominant transmission of the Alpha and Delta SARS-CoV-2 variants and some Omicron variant sublineages. Audio recordings of volitional coughs, exhalations, and speech were collected in the 'Speak up to help beat coronavirus' digital survey alongside demographic, self-reported symptom and respiratory condition data, and linked to SARS-CoV-2 test results. The UK COVID-19 Vocal Audio Dataset represents the largest collection of SARS-CoV-2 PCR-referenced audio recordings to date. PCR results were linked to 70,794 of 72,999 participants and 24,155 of 25,776 positive cases. Respiratory symptoms were reported by 45.62% of participants. This dataset has additional potential uses for bioacoustics research, with 11.30% participants reporting asthma, and 27.20% with linked influenza PCR test results., Comment: 39 pages, 4 figures

Recent work has reported that AI classifiers trained on audio recordings can accurately predict severe acute respiratory syndrome coronavirus 2 (SARSCoV2) infection status. Here, we undertake a large scale study of audio-based deep learning classifiers, as part of the UK governments pandemic response. We collect and analyse a dataset of audio recordings from 67,842 individuals with linked metadata, including reverse transcription polymerase chain reaction (PCR) test outcomes, of whom 23,514 tested positive for SARS CoV 2. Subjects were recruited via the UK governments National Health Service Test-and-Trace programme and the REal-time Assessment of Community Transmission (REACT) randomised surveillance survey. In an unadjusted analysis of our dataset AI classifiers predict SARS-CoV-2 infection status with high accuracy (Receiver Operating Characteristic Area Under the Curve (ROCAUC) 0.846 [0.838, 0.854]) consistent with the findings of previous studies. However, after matching on measured confounders, such as age, gender, and self reported symptoms, our classifiers performance is much weaker (ROC-AUC 0.619 [0.594, 0.644]). Upon quantifying the utility of audio based classifiers in practical settings, we find them to be outperformed by simple predictive scores based on user reported symptoms.

Since early in the coronavirus disease 2019 (COVID-19) pandemic, there has been interest in using artificial intelligence methods to predict COVID-19 infection status based on vocal audio signals, for example cough recordings. However, existing studies have limitations in terms of data collection and of the assessment of the performances of the proposed predictive models. This paper rigorously assesses state-of-the-art machine learning techniques used to predict COVID-19 infection status based on vocal audio signals, using a dataset collected by the UK Health Security Agency. This dataset includes acoustic recordings and extensive study participant meta-data. We provide guidelines on testing the performance of methods to classify COVID-19 infection status based on acoustic features and we discuss how these can be extended more generally to the development and assessment of predictive methods based on public health datasets.

World models power some of the most efficient reinforcement learning algorithms. In this work, we showcase that they can be harnessed for continual learning - a situation when the agent faces changing environments. World models typically employ a replay buffer for training, which can be naturally extended to continual learning. We systematically study how different selective experience replay methods affect performance, forgetting, and transfer. We also provide recommendations regarding various modeling options for using world models. The best set of choices is called Continual-Dreamer, it is task-agnostic and utilizes the world model for continual exploration. Continual-Dreamer is sample efficient and outperforms state-of-the-art task-agnostic continual reinforcement learning methods on Minigrid and Minihack benchmarks., Comment: Accepted at CoLLAs 2023, 21 pages, 15 figures

Building generally capable agents is a grand challenge for deep reinforcement learning (RL). To approach this challenge practically, we outline two key desiderata: 1) to facilitate generalization, exploration should be task agnostic; 2) to facilitate scalability, exploration policies should collect large quantities of data without costly centralized retraining. Combining these two properties, we introduce the reward-free deployment efficiency setting, a new paradigm for RL research. We then present CASCADE, a novel approach for self-supervised exploration in this new setting. CASCADE seeks to learn a world model by collecting data with a population of agents, using an information theoretic objective inspired by Bayesian Active Learning. CASCADE achieves this by specifically maximizing the diversity of trajectories sampled by the population through a novel cascading objective. We provide theoretical intuition for CASCADE which we show in a tabular setting improves upon na\"ive approaches that do not account for population diversity. We then demonstrate that CASCADE collects diverse task-agnostic datasets and learns agents that generalize zero-shot to novel, unseen downstream tasks on Atari, MiniGrid, Crafter and the DM Control Suite. Code and videos are available at https://ycxuyingchen.github.io/cascade/, Comment: To be published at NeurIPS 2022. Code and videos available at https://ycxuyingchen.github.io/cascade/

Cross-sectional strategies are a classical and popular trading style, with recent high performing variants incorporating sophisticated neural architectures. While these strategies have been applied successfully to data-rich settings involving mature assets with long histories, deploying them on instruments with limited samples generally produce over-fitted models with degraded performance. In this paper, we introduce Fused Encoder Networks -- a novel and hybrid parameter-sharing transfer ranking model. The model fuses information extracted using an encoder-attention module operated on a source dataset with a similar but separate module focused on a smaller target dataset of interest. This mitigates the issue of models with poor generalisability that are a consequence of training on scarce target data. Additionally, the self-attention mechanism enables interactions among instruments to be accounted for, not just at the loss level during model training, but also at inference time. Focusing on momentum applied to the top ten cryptocurrencies by market capitalisation as a demonstrative use-case, the Fused Encoder Networks outperforms the reference benchmarks on most performance measures, delivering a three-fold boost in the Sharpe ratio over classical momentum as well as an improvement of approximately 50% against the best benchmark model without transaction costs. It continues outperforming baselines even after accounting for the high transaction costs associated with trading cryptocurrencies., Comment: 18 pages, 12 figures

The ACM Multimedia 2022 Computational Paralinguistics Challenge addresses four different problems for the first time in a research competition under well-defined conditions: In the Vocalisations and Stuttering Sub-Challenges, a classification on human non-verbal vocalisations and speech has to be made; the Activity Sub-Challenge aims at beyond-audio human activity recognition from smartwatch sensor data; and in the Mosquitoes Sub-Challenge, mosquitoes need to be detected. We describe the Sub-Challenges, baseline feature extraction, and classifiers based on the usual ComPaRE and BoAW features, the auDeep toolkit, and deep feature extraction from pre-trained CNNs using the DeepSpectRum toolkit; in addition, we add end-to-end sequential modelling, and a log-mel-128-BNN., Comment: 5 pages, part of the ACM Multimedia 2022 Grand Challenge "The ACM Multimedia 2022 Computational Paralinguistics Challenge (ComParE 2022)"

Training agents in cooperative settings offers the promise of AI agents able to interact effectively with humans (and other agents) in the real world. Multi-agent reinforcement learning (MARL) has the potential to achieve this goal, demonstrating success in a series of challenging problems. However, whilst these advances are significant, the vast majority of focus has been on the self-play paradigm. This often results in a coordination problem, caused by agents learning to make use of arbitrary conventions when playing with themselves. This means that even the strongest self-play agents may have very low cross-play with other agents, including other initializations of the same algorithm. In this paper we propose to solve this problem by adapting agent strategies on the fly, using a posterior belief over the other agents' strategy. Concretely, we consider the problem of selecting a strategy from a finite set of previously trained agents, to play with an unknown partner. We propose an extension of the classic statistical technique, Gibbs sampling, to update beliefs about other agents and obtain close to optimal ad-hoc performance. Despite its simplicity, our method is able to achieve strong cross-play with unseen partners in the challenging card game of Hanabi, achieving successful ad-hoc coordination without knowledge of the partner's strategy a priori., Comment: Extended abstract published in AAMAS 2022

We introduce the Momentum Transformer, an attention-based deep-learning architecture, which outperforms benchmark time-series momentum and mean-reversion trading strategies. Unlike state-of-the-art Long Short-Term Memory (LSTM) architectures, which are sequential in nature and tailored to local processing, an attention mechanism provides our architecture with a direct connection to all previous time-steps. Our architecture, an attention-LSTM hybrid, enables us to learn longer-term dependencies, improves performance when considering returns net of transaction costs and naturally adapts to new market regimes, such as during the SARS-CoV-2 crisis. Via the introduction of multiple attention heads, we can capture concurrent regimes, or temporal dynamics, which are occurring at different timescales. The Momentum Transformer is inherently interpretable, providing us with greater insights into our deep-learning momentum trading strategy, including the importance of different factors over time and the past time-steps which are of the greatest significance to the model., Comment: included motivation for attention mechanism and additional architecture details

Local volatility is a versatile option pricing model due to its state dependent diffusion coefficient. Calibration is, however, non-trivial as it involves both proposing a hypothesis model of the latent function and a method for fitting it to data. In this paper we present novel Bayesian inference with Gaussian process priors. We obtain a rich representation of the local volatility function with a probabilistic notion of uncertainty attached to the calibrate. We propose an inference algorithm and apply our approach to S&P 500 market data., Comment: arXiv admin note: text overlap with arXiv:1901.06021

Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed Neural Networks (PINNs) to tackle such problems as they provide numerous benefits over traditional numerical approaches. Despite their potential benefits for solving differential equations, transfer learning has been under explored. In this study, we present a general framework for transfer learning PINNs that results in one-shot inference for linear systems of both ordinary and partial differential equations. This means that highly accurate solutions to many unknown differential equations can be obtained instantaneously without retraining an entire network. We demonstrate the efficacy of the proposed deep learning approach by solving several real-world problems, such as first- and second-order linear ordinary equations, the Poisson equation, and the time-dependent Schrodinger complex-value partial differential equation., Comment: ICML AI4Science Workshop 2022

This paper presents the first large-scale multi-species dataset of acoustic recordings of mosquitoes tracked continuously in free flight. We present 20 hours of audio recordings that we have expertly labelled and tagged precisely in time. Significantly, 18 hours of recordings contain annotations from 36 different species. Mosquitoes are well-known carriers of diseases such as malaria, dengue and yellow fever. Collecting this dataset is motivated by the need to assist applications which utilise mosquito acoustics to conduct surveys to help predict outbreaks and inform intervention policy. The task of detecting mosquitoes from the sound of their wingbeats is challenging due to the difficulty in collecting recordings from realistic scenarios. To address this, as part of the HumBug project, we conducted global experiments to record mosquitoes ranging from those bred in culture cages to mosquitoes captured in the wild. Consequently, the audio recordings vary in signal-to-noise ratio and contain a broad range of indoor and outdoor background environments from Tanzania, Thailand, Kenya, the USA and the UK. In this paper we describe in detail how we collected, labelled and curated the data. The data is provided from a PostgreSQL database, which contains important metadata such as the capture method, age, feeding status and gender of the mosquitoes. Additionally, we provide code to extract features and train Bayesian convolutional neural networks for two key tasks: the identification of mosquitoes from their corresponding background environments, and the classification of detected mosquitoes into species. Our extensive dataset is both challenging to machine learning researchers focusing on acoustic identification, and critical to entomologists, geo-spatial modellers and other domain experts to understand mosquito behaviour, model their distribution, and manage the threat they pose to humans., Comment: Accepted at the 35th Conference on Neural Information Processing Systems (NeurIPS 2021) Track on Datasets and Benchmarks. 10 pages main, 39 pages including appendix. This paper accompanies the dataset found at https://zenodo.org/record/4904800 with corresponding code at https://github.com/HumBug-Mosquito/HumBugDB

Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and other flexible function approximators. Despite these advances, learning remains computationally expensive due to the sequential nature of SDE integrators. In this work, we propose an importance-sampling estimator for probabilities of observations of SDEs for the purposes of learning. Crucially, the approach we suggest does not rely on such integrators. The proposed method produces lower-variance gradient estimates compared to algorithms based on SDE integrators and has the added advantage of being embarrassingly parallelizable. This facilitates the effective use of large-scale parallel hardware for massive decreases in computation time.

Offline reinforcement learning enables agents to leverage large pre-collected datasets of environment transitions to learn control policies, circumventing the need for potentially expensive or unsafe online data collection. Significant progress has been made recently in offline model-based reinforcement learning, approaches which leverage a learned dynamics model. This typically involves constructing a probabilistic model, and using the model uncertainty to penalize rewards where there is insufficient data, solving for a pessimistic MDP that lower bounds the true MDP. Existing methods, however, exhibit a breakdown between theory and practice, whereby pessimistic return ought to be bounded by the total variation distance of the model from the true dynamics, but is instead implemented through a penalty based on estimated model uncertainty. This has spawned a variety of uncertainty heuristics, with little to no comparison between differing approaches. In this paper, we compare these heuristics, and design novel protocols to investigate their interaction with other hyperparameters, such as the number of models, or imaginary rollout horizon. Using these insights, we show that selecting these key hyperparameters using Bayesian Optimization produces superior configurations that are vastly different to those currently used in existing hand-tuned state-of-the-art methods, and result in drastically stronger performance., Comment: Spotlight @ ICLR 2022; Spotlight @ RL4RealLife Workshop ICML2021

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant improvement over other approaches in predicting trajectories of physical systems. These methods generally tackle autonomous systems that depend implicitly on time or systems for which a control signal is known apriori. Despite this success, many real world dynamical systems are non-autonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such non-autonomous systems by embedding the port-Hamiltonian formalism into neural networks, a versatile framework that can capture energy dissipation and time-dependent control forces. We show that the proposed \emph{port-Hamiltonian neural network} can efficiently learn the dynamics of nonlinear physical systems of practical interest and accurately recover the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient. A promising outcome of our network is its ability to learn and predict chaotic systems such as the Duffing equation, for which the trajectories are typically hard to learn., Comment: [under review]

Despite a series of recent successes in reinforcement learning (RL), many RL algorithms remain sensitive to hyperparameters. As such, there has recently been interest in the field of AutoRL, which seeks to automate design decisions to create more general algorithms. Recent work suggests that population based approaches may be effective AutoRL algorithms, by learning hyperparameter schedules on the fly. In particular, the PB2 algorithm is able to achieve strong performance in RL tasks by formulating online hyperparameter optimization as time varying GP-bandit problem, while also providing theoretical guarantees. However, PB2 is only designed to work for continuous hyperparameters, which severely limits its utility in practice. In this paper we introduce a new (provably) efficient hierarchical approach for optimizing both continuous and categorical variables, using a new time-varying bandit algorithm specifically designed for the population based training regime. We evaluate our approach on the challenging Procgen benchmark, where we show that explicitly modelling dependence between data augmentation and other hyperparameters improves generalization.

Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive for larger datasets. We propose a Bayesian Quadrature scheme to make this marginalisation more efficient and thereby more practical. Through use of the maximum mean discrepancies between distributions, we define a kernel over kernels that captures invariances between Spectral Mixture (SM) Kernels. Kernel samples are selected by generalising an information-theoretic acquisition function for warped Bayesian Quadrature. We show that our framework achieves more accurate predictions with better calibrated uncertainty than state-of-the-art baselines, especially when given limited (wall-clock) time budgets.

Continual Learning (CL) considers the problem of training an agent sequentially on a set of tasks while seeking to retain performance on all previous tasks. A key challenge in CL is catastrophic forgetting, which arises when performance on a previously mastered task is reduced when learning a new task. While a variety of methods exist to combat forgetting, in some cases tasks are fundamentally incompatible with each other and thus cannot be learnt by a single policy. This can occur, in reinforcement learning (RL) when an agent may be rewarded for achieving different goals from the same observation. In this paper we formalize this "interference" as distinct from the problem of forgetting. We show that existing CL methods based on single neural network predictors with shared replay buffers fail in the presence of interference. Instead, we propose a simple method, OWL, to address this challenge. OWL learns a factorized policy, using shared feature extraction layers, but separate heads, each specializing on a new task. The separate heads in OWL are used to prevent interference. At test time, we formulate policy selection as a multi-armed bandit problem, and show it is possible to select the best policy for an unknown task using feedback from the environment. The use of bandit algorithms allows the OWL agent to constructively re-use different continually learnt policies at different times during an episode. We show in multiple RL environments that existing replay based CL methods fail, while OWL is able to achieve close to optimal performance when training sequentially., Comment: Accepted as an oral at AAAI 2022. 17 pages and 12 figures

ResNets constrained to be bi-Lipschitz, that is, approximately distance preserving, have been a crucial component of recently proposed techniques for deterministic uncertainty quantification in neural models. We show that theoretical justifications for recent regularisation schemes trying to enforce such a constraint suffer from a crucial flaw -- the theoretical link between the regularisation scheme used and bi-Lipschitzness is only valid under conditions which do not hold in practice, rendering existing theory of limited use, despite the strong empirical performance of these models. We provide a theoretical explanation for the effectiveness of these regularisation schemes using a frequency analysis perspective, showing that under mild conditions these schemes will enforce a lower Lipschitz bound on the low-frequency projection of images. We then provide empirical evidence supporting our theoretical claims, and perform further experiments which demonstrate that our broader conclusions appear to hold when some of the mathematical assumptions of our proof are relaxed, corresponding to the setup used in prior work. In addition, we present a simple constructive algorithm to search for counter examples to the distance preservation condition, and discuss possible implications of our theory for future model design., Comment: Main paper 10 pages including references, appendix 10 pages. 7 figures and 6 tables including appendix

Momentum strategies are an important part of alternative investments and are at the heart of commodity trading advisors (CTAs). These strategies have, however, been found to have difficulties adjusting to rapid changes in market conditions, such as during the 2020 market crash. In particular, immediately after momentum turning points, where a trend reverses from an uptrend (downtrend) to a downtrend (uptrend), time-series momentum (TSMOM) strategies are prone to making bad bets. To improve the response to regime change, we introduce a novel approach, where we insert an online changepoint detection (CPD) module into a Deep Momentum Network (DMN) [1904.04912] pipeline, which uses an LSTM deep-learning architecture to simultaneously learn both trend estimation and position sizing. Furthermore, our model is able to optimise the way in which it balances 1) a slow momentum strategy which exploits persisting trends, but does not overreact to localised price moves, and 2) a fast mean-reversion strategy regime by quickly flipping its position, then swapping it back again to exploit localised price moves. Our CPD module outputs a changepoint location and severity score, allowing our model to learn to respond to varying degrees of disequilibrium, or smaller and more localised changepoints, in a data driven manner. Back-testing our model over the period 1995-2020, the addition of the CPD module leads to an improvement in Sharpe ratio of one-third. The module is especially beneficial in periods of significant nonstationarity, and in particular, over the most recent years tested (2015-2020) the performance boost is approximately two-thirds. This is interesting as traditional momentum strategies have been underperforming in this period., Comment: minor changes made to methodology to match implementation

The performance of a cross-sectional currency strategy depends crucially on accurately ranking instruments prior to portfolio construction. While this ranking step is traditionally performed using heuristics, or by sorting the outputs produced by pointwise regression or classification techniques, strategies using Learning to Rank algorithms have recently presented themselves as competitive and viable alternatives. Although the rankers at the core of these strategies are learned globally and improve ranking accuracy on average, they ignore the differences between the distributions of asset features over the times when the portfolio is rebalanced. This flaw renders them susceptible to producing sub-optimal rankings, possibly at important periods when accuracy is actually needed the most. For example, this might happen during critical risk-off episodes, which consequently exposes the portfolio to substantial, unwanted drawdowns. We tackle this shortcoming with an analogous idea from information retrieval: that a query's top retrieved documents or the local ranking context provide vital information about the query's own characteristics, which can then be used to refine the initial ranked list. In this work, we use a context-aware Learning-to-rank model that is based on the Transformer architecture to encode top/bottom ranked assets, learn the context and exploit this information to re-rank the initial results. Backtesting on a slate of 31 currencies, our proposed methodology increases the Sharpe ratio by around 30% and significantly enhances various performance metrics. Additionally, this approach also improves the Sharpe ratio when separately conditioning on normal and risk-off market states., Comment: 10 pages, 4 figures

Reinforcement learning from large-scale offline datasets provides us with the ability to learn policies without potentially unsafe or impractical exploration. Significant progress has been made in the past few years in dealing with the challenge of correcting for differing behavior between the data collection and learned policies. However, little attention has been paid to potentially changing dynamics when transferring a policy to the online setting, where performance can be up to 90% reduced for existing methods. In this paper we address this problem with Augmented World Models (AugWM). We augment a learned dynamics model with simple transformations that seek to capture potential changes in physical properties of the robot, leading to more robust policies. We not only train our policy in this new setting, but also provide it with the sampled augmentation as a context, allowing it to adapt to changes in the environment. At test time we learn the context in a self-supervised fashion by approximating the augmentation which corresponds to the new environment. We rigorously evaluate our approach on over 100 different changed dynamics settings, and show that this simple approach can significantly improve the zero-shot generalization of a recent state-of-the-art baseline, often achieving successful policies where the baseline fails., Comment: Accepted @ ICML 2021; Spotlight @ ICLR 2021 "Self-Supervision for Reinforcement Learning Workshop"

Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this paper we present a framework to analyse adversarial robustness of GPs, defined as invariance of the model's decision to bounded perturbations. Given a compact subset of the input space $T\subseteq \mathbb{R}^d$, a point $x^*$ and a GP, we provide provable guarantees of adversarial robustness of the GP by computing lower and upper bounds on its prediction range in $T$. We develop a branch-and-bound scheme to refine the bounds and show, for any $\epsilon > 0$, that our algorithm is guaranteed to converge to values $\epsilon$-close to the actual values in finitely many iterations. The algorithm is anytime and can handle both regression and classification tasks, with analytical formulation for most kernels used in practice. We evaluate our methods on a collection of synthetic and standard benchmark datasets, including SPAM, MNIST and FashionMNIST. We study the effect of approximate inference techniques on robustness and demonstrate how our method can be used for interpretability. Our empirical results suggest that the adversarial robustness of GPs increases with accurate posterior estimation., Comment: Submitted for publication