Extended Predictable Feature Analysis (PFAx) [Richthofer and Wiskott, 2017] is an extension of PFA [Richthofer and Wiskott, 2015] that allows generating a goal-directed control signal of an agent whose dynamics has previously been learned during a training phase in an unsupervised manner. PFAx hardly requires assumptions or prior knowledge of the agent's sensor or control mechanics, or of the environment. It selects features from a high-dimensional input by intrinsic predictability and organizes them into a reasonably low-dimensional model. While PFA obtains a well predictable model, PFAx yields a model ideally suited for manipulations with predictable outcome. This allows for goal-directed manipulation of an agent and thus for local navigation, i.e. for reaching states where intermediate actions can be chosen by a permanent descent of distance to the goal. The approach is limited when it comes to global navigation, e.g. involving obstacles or multiple rooms. In this article, we extend theoretical results from [Sprekeler and Wiskott, 2008], enabling PFAx to perform stable global navigation. So far, the most widely exploited characteristic of Slow Feature Analysis (SFA) was that slowness yields invariances. We focus on another fundamental characteristics of slow signals: They tend to yield monotonicity and one significant property of monotonicity is that local optimization is sufficient to find a global optimum. We present an SFA-based algorithm that structures an environment such that navigation tasks hierarchically decompose into subgoals. Each of these can be efficiently achieved by PFAx, yielding an overall global solution of the task. The algorithm needs to explore and process an environment only once and can then perform all sorts of navigation tasks efficiently. We support this algorithm by mathematical theory and apply it to different problems.
@cite_0 and @cite_39 use diverse density to discover bottleneck states as useful subgoals for RL tasks. This has some parallels to the algorithm in this paper in the sense that bottlenecks occur as special states. In we explicitly study the behavior of SFA around a bottleneck and suggest in a side note how slow features can be used as a bottleneck detector.
@cite_0 @cite_39
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This paper presents a method by which a reinforcement learning agent can automatically discover certain types of subgoals online. By creating useful new subgoals while learning, the agent is able to accelerate learning on the current task and to transfer its expertise to other, related tasks through the reuse of its ability to attain subgoals. The agent discovers subgoals based on commonalities across multiple paths to a solution. We cast the task of finding these commonalities as a multiple-instance learning problem and use the concept of diverse density to find solutions. We illustrate this approach using several gridworld tasks. Temporally extended actions (e.g., macro actions) have proven very useful for speeding up learning, ensuring robustness and building prior knowledge into AI systems. The options framework (Precup, 2000; Sutton, Precup & Singh, 1999) provides a natural way of incorporating such actions into reinforcement learning systems, but leaves open the issue of howgood options might be identified. In this paper, we empirically explore a simple approach to creating options. The underlying assumption is that the agent will be asked to perform different goalachievement tasks in an environment that is otherwise the same over time. Our approach is based on the intuition that states that are frequently visited on system trajectories, could prove to be useful subgoals (e.g., McGovern & Barto, 2001; Iba, 1989).We propose a greedy algorithm for identifying subgoals based on state visitation counts. We present empirical studies of this approach in two gridworld navigation tasks. One of the environments we explored contains bottleneck states, and the algorithm indeed finds these states, as expected. The second environment is an empty gridworld with no obstacles. Although the environment does not contain any obvious subgoals, our approach still finds useful options, which essentially allow the agent to explore the environment more quickly.