# Reinforcement learning with incremental action space

Let's say we have a problem which can be solved by some RL algorithms (DQN, for example, because we have discrete action space). At first, the action space is fixed (the number of actions is $$n_1$$), and we have already well trained an offline DQN model. Later, we have to add more actions for some reasons (and the number of action is now $$n_2$$, where $$n_2 > n_1$$).

Are there some solutions to update the value function or policy (or the neural network) with only minor changes?

Is there some solutions to update the model with only minor changes?

In general, assuming the new action choices are meaningful - in at least some states, the expected return from taking one of the new actions is higher than the current optimal policy using just the old action selection - then the answer here is "no".

At the very least you will need to re-train your agent such that it explores the new action choices, and learns the new value function and policy. You can of course start this re-training using data and internal representations learned from the earlier environment, and that may help if the new actions have not changed things too radically.

There are a couple of things that might help improve performance on this re-training:

• If the actions are not entirely discrete, but have some features that could be generalised from, you could base your value function or policy function estimators on those features instead of discrete actions. So for example in DQN your input to the neural network would be concatenated state, action feature vectors, and output a single value. Then it may generalise to the new actions quickly, in some cases perhaps even getting close to the correct value estimates from the start.

• If you were training using DynaQ+, this includes an exploration term (which is added to planning assessments of immediate reward) that will prioritise exploring new state/action pairs when they appear. Other planning algorithms may have similar adjustments, although I am not aware of specific ones that could be dropped straight into a DQN agent.

If you know in advance which states the new actions are likely to be most useful in, you may be able to insert that knowledge into some initial action selection or value estimate helpers to avoid the need to train from scratch.