Reductive MDPs: A Perspective Beyond Temporal Horizons

Solving general Markov decision processes (MDPs) is a computationally hard problem. Solving finite-horizon MDPs, on the other hand, is highly tractable with well known polynomial-time algorithms. What drives this extreme disparity, and do problems exist that lie between these diametrically opposed complexities? In this paper we identify and analyse a sub-class of stochastic shortest path problems (SSPs) for general state-action spaces whose dynamics satisfy a particular drift condition. This construction generalises the traditional, temporal notion of a horizon via decreasing reachability: a property called reductivity. It is shown that optimal policies can be recovered in polynomial-time for reductive SSPs -- via an extension of backwards induction -- with an efficient analogue in reductive MDPs. The practical considerations of the proposed approach are discussed, and numerical verification provided on a canonical optimal liquidation problem.

Reward is not enough: can we liberate AI from the reinforcement learning paradigm?

I present arguments against the hypothesis put forward by Silver, Singh, Precup, and Sutton ( https://www.sciencedirect.com/science/article/pii/S0004370221000862 ) : reward maximization is not enough to explain many activities associated with natural and artificial intelligence including knowledge, learning, perception, social intelligence, evolution, language, generalisation and imitation. I show such reductio ad lucrum has its intellectual origins in the political economy of Homo economicus and substantially overlaps with the radical version of behaviourism. I show why the reinforcement learning paradigm, despite its demonstrable usefulness in some practical application, is an incomplete framework for intelligence -- natural and artificial. Complexities of intelligent behaviour are not simply second-order complications on top of reward maximisation. This fact has profound implications for the development of practically usable, smart, safe and robust artificially intelligent agents.