This looks really interesting. The first thought that jumped to mind was how this geometric principle might extend to abstract goal space in general. There is research suggesting that savannah-like environments may have provided human evolution ideal selective pressures for developing the cognitive tools necessary for making complex plans. Becoming adept at navigating physical scenes with obstacles, predators, refuges, and prey gave humans the right kind of brain architecture for also navigating abstract spaces full of abstract goals, anti-goals (bad outcomes to avoid), obstacles, and paths (plans).
The “geometric decision making” in the paper was studied for physical spaces, but I could imagine that animal minds (including humans) use such a bifurcation method in other goal spaces as well. In other words, agents would start out traversing state space toward the average of multiple, moderately distant goals (seeking a state from which multiple goals are still achievable), then would switch to choosing a sub-cluster of the goals to pursue once they get close enough (the binary decision / bifurcation point). This would iterate until the agent has only one easily achievable goal in front of it.
My guess is that this strategy would be safer than choosing a single goal among many at the outset of planning (e.g., the one goal with the highest expected utility upon achievement). If the situation changes while the agent is in the middle of pursuing a goal, it might find itself too far away from any other goal to make up for the sunk cost. If instead it had been pursuing some sort of multi-goal-centroid state, it could still achieve a decent alternative goal even when what would have been its first choice ceases to be an option. As it gets closer to the multi-goal-centroid, it can afford to focus on just a subset (or just a single goal), since it knows that other decent options are still nearby in state space.
This looks really interesting. The first thought that jumped to mind was how this geometric principle might extend to abstract goal space in general. There is research suggesting that savannah-like environments may have provided human evolution ideal selective pressures for developing the cognitive tools necessary for making complex plans. Becoming adept at navigating physical scenes with obstacles, predators, refuges, and prey gave humans the right kind of brain architecture for also navigating abstract spaces full of abstract goals, anti-goals (bad outcomes to avoid), obstacles, and paths (plans).
The “geometric decision making” in the paper was studied for physical spaces, but I could imagine that animal minds (including humans) use such a bifurcation method in other goal spaces as well. In other words, agents would start out traversing state space toward the average of multiple, moderately distant goals (seeking a state from which multiple goals are still achievable), then would switch to choosing a sub-cluster of the goals to pursue once they get close enough (the binary decision / bifurcation point). This would iterate until the agent has only one easily achievable goal in front of it.
My guess is that this strategy would be safer than choosing a single goal among many at the outset of planning (e.g., the one goal with the highest expected utility upon achievement). If the situation changes while the agent is in the middle of pursuing a goal, it might find itself too far away from any other goal to make up for the sunk cost. If instead it had been pursuing some sort of multi-goal-centroid state, it could still achieve a decent alternative goal even when what would have been its first choice ceases to be an option. As it gets closer to the multi-goal-centroid, it can afford to focus on just a subset (or just a single goal), since it knows that other decent options are still nearby in state space.