Combining Optimal Path Search With Task-Dependent Learning in a Neural Network
This work addresses the limitation of conventional planning methods in handling adaptive cost changes for tasks like navigation, offering a novel integration of path finding and learning, though it appears incremental as it builds on existing algorithms like Bellman-Ford.
The paper tackles the problem of finding optimal paths in graphs with adaptive costs by proposing a neural network representation that transforms costs into synaptic weights, enabling online adaptation via learning mechanisms like Hebbian learning, and demonstrates it achieves identical solutions to the Bellman-Ford algorithm while allowing task-dependent path augmentation in navigation and sequence-following tasks.
Finding optimal paths in connected graphs requires determining the smallest total cost for traveling along the graph's edges. This problem can be solved by several classical algorithms where, usually, costs are predefined for all edges. Conventional planning methods can, thus, normally not be used when wanting to change costs in an adaptive way following the requirements of some task. Here we show that one can define a neural network representation of path finding problems by transforming cost values into synaptic weights, which allows for online weight adaptation using network learning mechanisms. When starting with an initial activity value of one, activity propagation in this network will lead to solutions, which are identical to those found by the Bellman-Ford algorithm. The neural network has the same algorithmic complexity as Bellman-Ford and, in addition, we can show that network learning mechanisms (such as Hebbian learning) can adapt the weights in the network augmenting the resulting paths according to some task at hand. We demonstrate this by learning to navigate in an environment with obstacles as well as by learning to follow certain sequences of path nodes. Hence, the here-presented novel algorithm may open up a different regime of applications where path-augmentation (by learning) is directly coupled with path finding in a natural way.