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Title: Multi-Advisor Reinforcement Learning

Paper content:
We consider tackling a single-agent RL problem by distributing it to $n$ learners.
These learners, called advisors, endeavour to solve the problem from a different focus.
Their advice, taking the form of action values, is then communicated to an aggregator, which is in control of the system.
We show that the local planning method for the advisors is critical and that none of the ones found in the literature is flawless: the \textit{egocentric} planning overestimates values of states where the other advisors disagree, and the \textit{agnostic} planning is inefficient around danger zones.
We introduce a novel approach called \textit{empathic} and discuss its theoretical aspects.
We empirically examine and validate our theoretical findings on a fruit collection task.
When a person faces a complex and important problem, his individual problem solving abilities might not suffice.
He has to actively seek for advice around him: he might consult his relatives, browse different sources on the internet, and/or hire one or several people that are specialised in some aspects of the problem.
He then aggregates the technical, ethical and emotional advice in order to build an informed plan and to hopefully make the best possible decision.
A large number of papers tackle the decomposition of a single Reinforcement Learning task (RL, Sutton & Barto, 1998) into several simpler ones.
They generally follow a method where agents are trained independently and generally greedily to their local optimality, and are aggregated into a global policy by voting or averaging.
Recent works BID12 BID30 prove their ability to solve problems that are intractable otherwise.
Section 2 provides a survey of approaches and algorithms in this field.Formalised in Section 3, the Multi-Advisor RL (MAd-RL) partitions a single-agent RL into a MultiAgent RL problem BID22 , under the widespread divide & conquer paradigm.
Unlike Hierarchical RL BID2 BID19 BID4 , this approach gives them the role of advisor: providing an aggregator with the local Q-values for all actions.
The advisors are said to have a focus: reward function, state space, learning technique, etc.
The MAd-RL approach allows therefore to tackle the RL task from different focuses.When a person is consulted for an advice by a enquirer, he may answer egocentrically: as if he was in charge of next actions, agnostically: anticipating any future actions equally, or empathically: by considering the next actions of the enquirer.
The same approaches are modelled in the local advisors' planning methods.
Section 4 shows that the egocentric planning presents the severe theoretical shortcoming of inverting a max into a max in the global Bellman equation.
It leads to an overestimation of the values of states where the advisors disagree, and creates an attractor phenomenon, causing the system to remain static without any tie-breaking possibilities.
It is shown on a navigation task that attractors can be avoided by lowering the discount factor γ under a given value.
The agnostic planning BID30 has the drawback to be inefficient in dangerous environments, because it gets easily afraid of the controller performing a bad sequence of actions.
Finally, we introduce our novel empathic planning and show that it converges to the global optimal Bellman equation when all advisors are training on the full state space.van BID29 demonstrate on a fruit collection task that a distributed architecture significantly speeds up learning and converges to a better solution than non distributed baselines.
Section 5.2 extends those results and empirically validates our theoretical analysis: the egocentric planning gets stuck in attractors with high γ values; with low γ values, it gets high scores but is also very unstable as soon as some noise is introduced; the agnostic planning fails at efficiently gathering the fruits near the ghosts; despite lack of convergence guarantees with partial information in advisors' state space, our novel empathic planning also achieves high scores while being robust to noise.
This article presented MAd-RL, a common ground for the many recent and successful works decomposing a single-agent RL problem into simpler problems tackled by independent learners.
It focuses more specifically on the local planning performed by the advisors.
Three of them -two found in the literature and one novel -are discussed, analysed and empirically compared: egocentric, agnostic, and empathic.
The lessons to be learnt from the article are the following ones.The egocentric planning has convergence guarantees but overestimates the values of states where the advisors disagree.
As a consequence, it suffers from attractors: states where the no-op action is preferred to actions making progress on a subset of subtasks.
Some domains, such as resource scheduling, are identified as attractor-free, and some other domains, such as navigation, are set conditions on γ to guarantee the absence of attractor.
It is necessary to recall that an attractor-free setting means that the system will continue making progress towards goals as long as there are any opportunity to do so, not that the egocentric MAd-RL system will converge to the optimal solution.The agnostic planning also has convergence guarantees, and the local agnostic planning is equivalent to the global agnostic planning.
However, it may converge to bad solutions.
For instance, in dangerous environments, it considers all actions equally likely, it favours staying away from situation where a random sequence of actions has a significant chance of ending bad: crossing a bridge would be avoided.
Still, the agnostic planning simplicity enables the use of general value functions BID28 BID30 .The
empathic planning optimises the system according to the global Bellman optimality equation, but without any guarantee of convergence, if the advisor state space is smaller than the global state.In our experiments, we never encountered a case where the convergence was not obtained, and on the Pac-Boy domain, it robustly learns a near optimal policy after only 10 epochs. It
can also be safely applied to Ensemble RL tasks where all learners are given the full state space.

assistant: text: We consider tackling a single-agent RL problem by distributing it to $n$ learners.