November 15, 2018

Online Bayesian Deep Learning in Production at Tencent

Bayesian deep learning methods often look like a theoretical curiosity, rather than a practically useful tool, and I'm personally a bit skeptical about the practical usefulness of some of the work. However, there are some situations a decent method of handling and representing residual uncertainties about model parameters might prove crucial. These applications include active learning, reinforcement learning and online/continual learning.

So as I recently read a paper by Tencent, I was surprised to learn that the online Bayesian deep learning algorithm is apparently deployed in production to power click-through-rate prediction in their ad system. I thought, therefore, that this is worth a mention. Here is the paper:

Though the paper has a few typos and sometimes inconsistent notation (like going back and forth between using $\omega$ and $w$) which can make it tricky to read, I like the paper's layout: starting from desiderata - what the system has to be able to do - arriving at an elegant solution.

Assumed Density Filtering

The method relies on the approximate Bayesian online-learning technique often referred to as assumed density filtering.

ADF has been independently discovered by the statistics, machine learning and control communities (for citations see (Minka, 2001). It is perhaps most elegantly described by Opper, (1998), and by Minka, (2001) who also extended the idea to develop expectation propagation, a highly influential method for approximate Bayesian inference not just for online settings.

ADF can be explained as recursive algorithm repeating the following steps:

Probabilistic Backpropagation

The Tencent paper is based on probabilistic backpropagation (Hernandez-Lobato and Adams, 2015), which uses the ADF idea multiple times to perform the two non-trivial tasks required in a supervised Bayesian deep network: inference and learning.

I find the similarity of this algorithm to gradient calculations in neural network training beautiful: forward propagation to perform inference, forward and backward propagation for learning and parameter updates.

Crucially though, there is no gradient descent, or indeed no gradients or iterative optimization taking place here. After a single forward-backward cycle, information about the new datapoint (or minibatch of data) is - approximately - incorporated into the updated distribution $q_{t}(w)$ of network weights. Once this is done, the mini-batch can be discarded and never revisited. This makes this method a great candidate for online learning in large-scale streaming data situations.

Parallel operation

Another advantage of this method is that it can be parallelized in a data-parallel fashion: Multiple workers can update the posterior simultaneously on different minibatches of data. Expectation-propagation provides a meaningful way of combining the parameter updates computed by parallel workers in a meaningful fashion. Indeed, this is what the PBODL algorithm of Tencent does.


Bayesian online learning comes with great advantages. In recommender systems and ads marketplaces, the Bayesian online learning approach handles the user and item cold-start problem gracefully. If there is a new ad in the system that has to be recommended, initially our network might say "I don't really know", and then gradually hone in on a confident prediction as more data is observed.

One can use the uncertainty estimates in a Bayesian network to perform online learning: actively proposing which items to label in order to increase predictive performance in the future. In the context of ads, this may be a useful feature if implemented with care.

Finally, there is the useful principle that Bayes never forgets: if we perform exact Bayesian updates on global parameters of an exchangeable model, the posterior will store information indefinitely long about all datapoints, including very early ones. This advantage is clearly demonstrated in DeepMind's work on catastrophic forgetting (Kirkpatrick et al, 2017). This capacity to keep a long memory of course diminishes the more approximations we have to make, which leads me to drawbacks.


The ADF method is only approximate, and over time, the approximations in each step may accumulate resulting in the network to essentially forget what it learned from earlier datapoints. It is also worth pointing out that in stationary situations, the posterior over parameters is expected to shrink, especially in the last hidden layers of the network where there are often fewer parameters. This posterior compression is often countered by introducing explicit forgetting: without evidence to the contrary, the variance of each parameter is marginally increased in each step. Forgetting and the lack of infinite memory may turn out to be an advantage, not a bug, in non-stationary situations where more recent datapoints are more representative of future test cases.

A practical drawback of a method like this in production environments is that probabilistic forward- and backpropagation require non-trivial custom implementations. Probabilistic backprop does not use reverse mode automatic differentiation, i.e. vanilla backprop as a subroutine. As a consequence, one cannot rely on extensively tested and widely used autodiff packages in tensorflow or pytorch, and performing probabilistic backprop in new layer-types might require significant effort and custom implementations. It is possible that high-quality message passing packages such as the recently open-sourced will see a renaissance after all.

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