The Living Thing / Notebooks :

Bandit problems

Also reinforcement learning, and stochastic control

Bandit problems, Markov decision processes, a smattering of dynamic programming, game theory, optimal control, and online learning the solutions to such problems, esp. reinforcement learning.

Learning, where you must learn an optimal action in response to your stimulus, possibly an optimal “policy” of trying different actions over time, not just an MMSE-minimal prediction from complete data.

Comes in adversarial and stochastic flavours, apparently, although I’ve hit the boundaries of my knowledge there.

Pseudopolitical diversion

See clickbait bandits.



Conceptually, the base model here is a one- or many-armed poker machine. You can pop coins in, and each time you do you may pull an arm; you might get rewarded. Each arm of the machine might have different returns; but the only way to find out is to play.

How do you choose optimally which arms to pull and when? How much is to work spending to find the arm with the best return on investment, given that it costs to collect more data?

This can be formalised by minimizing regret and defining some other terms and what you get out is a formalized version of Skinnerian learning that you can easily implement as an algorithm and feel that you have got some satisfyingly optimal properties for.

The thing about whether to choose a new arm when you are on a known good one, or to switch to another one in hope of it being better, this is a symbolic one and it’s called the exploration/exploitation tradeoff.


Reinforcement learning with delayed reward

Richard Xu’s take:

  • No data label as in supervised learning, only a reward signal
  • feedback is delayed
  • data are not i.i.d. but sequentially dependent
  • agent’s actions affect the data it receives.

New tool by Microsoft: Multi-World Testing (MWT) appears to be an online learning problem that augments its data by re-using the data for offline testing:

… is a toolbox of machine learning technology for principled and efficient experimentation, plausibly applicable to most Microsoft services that interact with customers. In many scenarios, this technology is exponentially more efficient than the traditional A/B testing. The underlying research area, mature and yet very active, is known under many names: “multi-armed bandits”, “contextual bandits”, “associative reinforcement learning”, and “counterfactual evaluation”, among others.

To take an example, suppose one wants to optimize clicks on suggested news stories. To discover what works, one needs to explore over the possible news stories. Further, if the suggested news story can be chosen depending on the visitor’s profile, then one needs to explore over the possible “policies” that map profiles to news stories (and there are exponentially more “policies” than news stories!). Traditional ML fails at this because it does not explore. Whereas MWT allows you to explore continuously, and optimize your decisions using this exploration data.

It has a better introduction here, by John Langford: (cf ABCD15)

Removing the credit assignment problem from reinforcement learning yields the Contextual Bandit setting which we know is generically solvable in the same manner as common supervised learning problems. I know of about a half-dozen real-world successful contextual bandit applications typically requiring the cooperation of engineers and deeply knowledgeable data scientists.

Can we make this dramatically easier? We need a system that explores over appropriate choices with logging of features, actions, probabilities of actions, and outcomes. These must then be fed into an appropriate learning algorithm which trains a policy and then deploys the policy at the point of decision. Naturally, this is what we’ve done and now it can be used by anyone. This drops the barrier to use down to: “Do you have permissions? And do you have a reasonable idea of what a good feature is?”

A key foundational idea is Multiworld Testing: the capability to evaluate large numbers of policies mapping features to action in a manner exponentially more efficient than standard A/B testing. This is used pervasively in the Contextual Bandit literature and you can see it in action for the system we’ve made at Microsoft Research.



Bubeck again: Kernel-based methods for bandit convex optimization, part 1.


Ben Recht and Roy Frostig, Nesterov’s punctuation equilibrium:

In a landmark new paper by Salimans, Ho, Chen, and Sutskever from OpenAI, (SHCS17) the authors show that a particular class of genetic algorithms (called Evolutionary Strategies) gives excellent performance on a variety of reinforcement learning benchmarks. As optimizers, the application of genetic algorithms raises red flags and usually causes us to close browser windows. But fear not! As we will explain, the particular algorithm deployed happens to be a core method in optimization, and the fact that this method is successful sheds light on the peculiarities of reinforcement learning more than it does about genetic algorithms in general.

Deep reinforcement learning

Of course, artificial neural networks are a thing in this domain too.

Casual concrete example and intro by Mat Kelcey.

The trick is you approximate the action table in Q-learning using a neural net.

Implementation: keras-rl

Pseudopolitical diversion: Clickbait bandit problems

An application, esp for contextual bandits.

There is a lot of stuff being done in bandit problems specifically to model consumers and web pages; Therefore I’ll talk about it from that perspective:

The science of treating consumers of modern news media like what they are, near-passive objects of surveillance and control. Because trying to rely on peoples’ rationality and agency to get things done has a poor track record in recent history.

The “bandit problems” phrase comes, by the way, from an extension of the “one armed bandit”, the poker machine, into a mathematical model for exploring the world by pulling on the arms of a poker machine.

mazes we set them instead of dotcom startups.

Markov decision problems

Bellman and Howard’s classic discrete time control stochastic problem


Too many CPU cycles? Why not look at optimal control in this setting?

“A POMDP is a partially observable Markov decision process. It is a model, originating in the operations research (OR) literature, for describing planning tasks in which the decision maker does not have complete information as to its current state. The POMDP model provides a convenient way of reasoning about tradeoffs between actions to gain reward and actions to gain information.”


Vowpal Wabbit does contextual bandit learning.:

VW contains a contextual bandit module which allows you to optimize a predictor based on already collected contextual bandit data. In other words, the module does not handle the exploration issue, it assumes it can only use the currently available data previously collected from some “exploration” policy.

Multiple World Testing source code.

Sequential surrogate interactive model optimisation

Not what I think of here, but it and many other hyperparameter optimization-type problems have an RL interpretation. That is, you can use RL to learn the hyper parameters of your deep learning model. (This is not the same as deep learning of RL policies.) See Sequential surrogate model optimisation for more of that, or the papers JaTa15, LJDR16a, LJDR16b, FBBZ17.

To read

Agarwal, A., Bird, S., Cozowicz, M., Dudik, M., Langford, J., Li, L., … Slivkins, A. (2015) Introduction to Multi-World Testing.
Bellman, R. (1957) A Markovian decision process. . DTIC Document
Bellman, R., & Kalaba, R. (1961) A note on interrupted stochastic control processes. Information and Control, 4(4), 346–349. DOI.
Bottou, L. (2014) Learning to Interact. . Presented at the Microsoft Techfest
Bottou, L., Peters, J., Quiñonero-Candela, J., Charles, D. X., Chickering, D. M., Portugaly, E., … Snelson, E. (2013) Counterfactual Reasoning and Learning Systems: The Example of Computational Advertising. Journal of Machine Learning Research, 14, 3207–3260.
Bubeck, S., & Cesa-Bianchi, N. (2012) Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems. Foundations and Trends® in Machine Learning, 5(1), 1–122. DOI.
Bubeck, S., Munos, R., & Stoltz, G. (2011) Pure Exploration in Finitely–Armed and Continuous–Armed Bandits. Theoretical Computer Science, 412, 1832–1852.
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Li, L., Jamieson, K., DeSalvo, G., Rostamizadeh, A., & Talwalkar, A. (2016b) Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization. ArXiv:1603.06560 [Cs, Stat].
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