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Title: Value Propagation Networks

Paper content:
We present Value Propagation (VProp), a set of parameter-efficient differentiable planning modules built on Value Iteration which can successfully be trained using reinforcement learning to solve unseen tasks, has the capability to generalize to larger map sizes, and can learn to navigate in dynamic environments.
We show that the modules enable learning to plan when the environment also includes stochastic elements, providing a cost-efficient learning system to build low-level size-invariant planners for a variety of interactive navigation problems.
We evaluate on static and dynamic configurations of MazeBase grid-worlds, with randomly generated environments of several different sizes, and on a StarCraft navigation scenario, with more complex dynamics, and pixels as input.
Planning is a key component for artificial agents in a variety of domains.
However, a limit of classical planning algorithms is that one needs to know how to search for an optimal -or at least reasonable -solution for each instantiation of every possible type of plan.
As the environment dynamics and states complexity increase, this makes writing planners difficult, cumbersome, or simply entirely impractical.
This is among the reasons why "learning to plan" has been an active research area to address these shortcomings BID17 BID8 .
To be useful in practice we propose that methods that enable to learn planners should have at least two properties: they should be traces free, i.e. not require traces from an optimal planner, and they should generalize, i.e. learn planners that are able to function on plans of the same type but of unseen instance and/or planning horizons.In Reinforcement Learning (RL), learning to plan can be framed as the problem of finding a policy that maximises the expected return from the environment, where such policy is a greedy function that selects actions that will visit states with a higher value for the agent.
This in turns shifts the problem to the one of obtaining good estimates of state values.
One of the most commonly used algorithms to solve this problem is Value Iteration (VI), which estimates the state values by collecting and propagating the observed rewards until a fixed point is reached.
A policy -or a plan -can then be constructed by rolling out the obtained value function on the desired state-action pairs.When the environment can be represented as an occupancy map, a 2D grid, it is possible to approximate this planning algorithm using a deep convolutional neural network (CNN) to propagate the rewards on the grid cells.
This enables one to differentiate directly through the planner steps and perform end-to-end learning of the value function.
BID25 train such models -Value Iteration Networks (VIN) -with a supervised loss on the trace from a search/planning algorithm, with the goal to find the parameters that can solve the shortest path task in such environments by iteratively learning the value function using the convnet.
However, this baseline requires good target value estimates, violating our wished trace free property, and limiting its usage in interactive, dynamic settings.
Furthermore, it doesn't take advantage of the model structure to generalise to harder instances of the task.In this work we extend the formalization used in VIN to more accurately represent the structure of grid-world-like scenarios, enabling Value Iteration network modules to be naturally used within the reinforcement learning framework beyond the scope of the initial work, while also removing some of the limitations and underlying assumptions constraining the original architecture.
We show that our models can not only learn to plan and navigate in dynamic environments, but that their hierarchical structure provides a way to generalize to navigation tasks where the required planning horizon and the size of the map are much larger than the ones seen at training time.
Our main contributions include: (1) introducing VProp and MVProp, network planning modules which successfully learn to solve pathfinding tasks via reinforcement learning using minimal parametrization, (2) demonstrating the ability to generalize to large unseen maps when training exclusively on much smaller ones, and (3) showing that our modules can learn to plan in environments with more complex dynamics than a static grid world, both in terms of transition function and observation complexity.
Architectures that try to solve the large but structured space of navigation tasks have much to benefit from employing planners that can be learnt from data, however these need to be sample efficient to quickly adapt to local environment dynamics so that they can provide a flexible planning horizon without the need to collect new data.
Our work shows that such planners can be successfully learnt via Reinforcement Learning when the dynamics of the task are taken into account, and that great generalization capabilities can be expected when these models are applied to 2D path-planning tasks.
Furthermore, we have demonstrated that our methods can even generalize when the environment has dynamic, noisy, and adversarial elements, or with high-dimensional observation spaces, enabling them to be employed in relatively complex tasks.
A major issue that still prevents these planners from being deployed on harder tasks is computational cost, since the depth increases with the length of the path that agents must solve, however architectures employing VI modules as low level planners have been successfully tackling complex interactive tasks (Section 1.1), thus we expect our methods to provide a way for such type of work to train end-to-end via reinforcement learning, even for pathfinding tasks found in different graph-like structures (for which we have at least the relevant convolutional operators).
Finally, interesting venues where VProp and MVProp may be applied are mobile robotics and visual tracking BID3 , where our work could be used to learn arbitrary propagation functions, and model a wide range of potential functions.A More general graph structures VIN and VProp are, in their most general formulation, applicable to any graph-structured input.
They ultimately belong to the general class of graph convolutional neural networks, and several variations of the value iteration modules specifically tailored to non-regular graph structures have been proposed (see e.g., BID13 ).
The three equations for VProp (Sections 3.2, 3.1) are applicable to any graph structure, as long as there is a one-to-one mapping between nodes in the neighborhood of the current position and actions (which is usually the case in navigation problems).
Our work focuses on the simplest possible parametrization that is relevant in many navigation and pathfinding scenarios, while for more general graph structures, even assuming a deterministic model, the term p i,j v DISPLAYFORM0 to account for the edge weight between i, j and i , j .
For regular graph structures such as 2D grids, this can be included in the embedding function Φ, which outputs not just one parameter for each position but as many parameters as the neighborhood size.
Other possibilities include using an attention mechanism for graph-convolutional neural networks in place of p (see e.g., Tamar et al. (2016, section 4.4) ).
in such case, our method differs from the original VIN purely by the parametrization of the reward and the focus on the deterministic models, which we believe are relevant in navigation problems.

assistant: text: The paper presents an extension of the original value iteration networks (VIN) by considering a state-dependent transition function.