Connectionists: The Forgotten Role of Pareto

Tue Feb 11 12:34:02 EST 2014

There is an important issue that seems to be missing from the current discussions on Deep Belief Networks, Developmental Robotics, etc. This forgotten issue has received less attention in machine learning, developmental robotics, and neuroscience in general.

It is that an individual "explicitly" has conflicting objectives. I will call this explicit conflicting objectives as "Pareto" to differentiate it from taking a weighted sum to combine these objectives into one. I argue we lose a big opportunity when doing this mistake.

What a Pareto approach does? It allows many competing models/hypotheses to co-exist together as long as they explain different parts of the agent's utility. They co-exist because they "optimally" trade-off the conflicting objectives of the agent "differently".

In a way, this idea of Pareto learning [1] provides a principled approach to combining models and forming ensembles [2], allowing the agent to dance (be adaptive) on this Pareto curve when faced with different environmental conditions [3] and swinging their decisions by selecting a model that is appropriate to the trade-off the agent requires in different environments.

It also seems natural to me that this Pareto approach gives us the ability as individuals to be flexible and defines new measures for robustness [4].
In fact, the idea in [3] "on reflection after 5 years since it was published" offers a cognitive architecture. The non-dominance set is the smallest number of models that need to be maintained within the long term memory (LTM). When the agent senses the trade-off in the environment, a sensory-semantic process kicks off and select the most appropriate model from the LTM to match the sensed trade-off, which can then send a code into a short term memory.

Also, on reflection, it seems a principled approach to form the society in Minsky's society of mind [5], because it does not require a hierarchy and it satisfies the non-compromise principle.

By limiting learning and evolution to a single objective, we limit the flexibility in the system to a single point on the trade-off curve; we lose a precious opportunity.

My hypothesis is, this conflict in the objectives that humans are faced with in their environment is a primary cause for many differentiation processes, be it biological, behavioural or cognitive. It is an essential component in the interaction between the agent and the environment, without which, we are stuck with one single model - even if it is made-up of many other models that "seem" on an arbitrarily defined measure to be different!

P.S. I differentiate between different environments or different environmental conditions and the same environment with different utilities. The reason is, from a multi-agent perspective, the utility - I would argue - sits at the interfaces among (interaction of) the agents, while the environment is everything that is outside the multi-agent (exogenous to the multiple agents as a group). I argue that utilities sit at the interface rather than within the agents because I believe that utilities are negotiated, they are not pre-determined.

1. Abbass H.A. (2003) Speeding up Back-Propagation Using Multiobjective Evolutionary Algorithms, Neural Computation, MIT Press, vol. 15, No 11, 2705-2726.

2. Abbass H.A. (2003) "Pareto neuro-ensembles." AI 2003: Advances in Artificial Intelligence. LNCS 2903, Springer Berlin Heidelberg. 554-566.

3. Abbass H.A. and Bender A. (2009) The Pareto Operating Curve for Risk Minimization, Artificial Life and Robotics Journal, Springer, 14(4), 449-452.
4. Bui L., Abbass H.A., Barlow M., and Bender A. (2012) Robustness Against the Decision-Maker's Attitude to Risk in Problems with Conflicting Objectives, IEEE Transactions on Evolutionary Computation, 16(1), 1-19.

5. Leu G., Curtis N., and Abbass H.A. Society of Mind cognitive agent architecture applied to drivers adapting in a traffic context, Adaptive Behaviour, to appear, online first doi: 10.1177/1059712313509652.

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