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Hanoi towers speed3/16/2023 ![]() ![]() ![]() We did find though that the performance of FBRL degraded for 3 discs, which may be due to overfitting.īehavior cloning of expert demonstrations can speed up learning optimal policies in a more sample-efficient way over reinforcement learning. When we increase the number of discs, FBRL outperforms DDQN. ![]() We again see an advantage for using FBRL as the goal gets further away. Figure 3 shows the results for running Towers of Hanoi with a different number of discs. For FBRL, we used 5 steps of imagination with 3 asynchronous streams. The model architecture is a fully-connected network with 100 outputs followed by RELU, followed by another fully-connected network with 9n outputs, representing the distribution over each bit. The backward model predicts a distribution for each bit over possible ∆ values: P (∆ = −1), P (∆ = 0), P (∆ = 1). For example, the environment in Figure 1 has a representation of since the small disc is on the first pillar and the large disc is on the third pillar. The inputs to the backward model are bit-strings indicating which pillars each disc is on. It receives a reward of 1 when all discs are in the third pillar and a step cost of −.01 per time-step. The actions are to move each disc to the first, second, or third pillar. In this problem, the agent needs to move n discs from the first to the third pillar, but it is only able to place a disc on top of another one if it is smaller than it. next environment we evaluate in is n-disc Towers of Hanoi. For comparison we formulate FBRL by augmented DDQN, which we compare against a standard DDQN. ![]() We evaluate our approach in Gridworld and Towers of Hanoi, il- lustrated in Figure 1. The purpose of our experiments is to demonstrate that FBRL can significantly speed up learning in environments with sparse rewards. As the system approaches the goal, the backward model will converge to the real model. As training progresses, the system will capture larger regional dynamics and start to predict potential global dynamics, e.g., presence of walls beyond what has been directly observed. Once discovered, the model will update and the value function will shift to anticipate the presence of the wall. While this is is inaccurate, it does provide a shape for the value function that will encourage traveling towards the goal until a wall is discovered. The hallucinated experience will likely predict movement through walls. Consider again the navigation problem, where the model in the immediate region will learn a factored representation for locomotion, but cannot predict the walls of the maze further away. In this way, it acts like an intrinsic reward to provide a predicted direction for exploration for the model. the model may start out being inaccurate, it provides a constantly improving signal that helps formulate the value function, which is then used to guide exploration. Can you calculate the number of moves it will take you to move the disks from one of the three poles to another?. Where's the MATH in this game? The number of separate transfers of single disks the priests must make to transfer the tower is 2 to the 64th minus 1, or 18,446,744,073,709,551,615 moves! If the priests worked day and night, making one move every second it would take slightly more than 580 billion years to accomplish the job! You have a great deal fewer disks than 64 here. A large disk could never be placed on top of a smaller one. Their assignment was to transfer the 64 disks from one of the three poles to another, with one important provision. Legend says that at the beginning of time the priests in the temple were given a stack of 64 gold disks, each one a little smaller than the one beneath it. Tower of Hanoi was inspired by a legend that tells of a Hindu temple where the pyramid puzzle might have been used for the mental discipline of young priests. You are allowed to move one piece at a time and are only allowed to place a smaller piece on top of a larger piece. Tower of Hanoi, also known as The Pagoda Puzzle, is an ancient puzzle that uses repetitive sequential moves for its solution. ![]()
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