This paper is a bit provocative (especially in the light of the recent DeepMind MuZero paper), and poses some interesting questions about the value of model-based planning. I'm not sure I agree with the overall argument it's making, but I think the experience of reading it made me hone my intuitions around why and when model-based planning should be useful. 

The overall argument of the paper is: rather than learning a dynamics model of the environment and then using that model to plan and learn a value/policy function from, we could instead just keep a large replay buffer of actual past transitions, and use that in lieu of model-sampled transitions to further update our reward estimators without having to acquire more actual experience. In this paper's framing, the central value of having a learned model is this ability to update our policy without needing more actual experience, and it argues that actual real transitions from the environment are more reliable and less likely to diverge than transitions from a learned parametric model. It basically sees a big buffer of transitions as an empirical environment model that it can sample from, in a roughly equivalent way to being able to sample transitions from a learnt model. 

An obvious counter-argument to this is the value of models in being able to simulate particular arbitrary trajectories (for example, potential actions you could take from your current point, as is needed for Monte Carlo Tree Search). Simply keeping around a big stock of historical transitions doesn't serve the use case of being able to get a probable next state *for a particular transition*, both because we might not have that state in our data, and because we don't have any way, just given a replay buffer, of knowing that an available state comes after an action if we haven't seen that exact combination before. (And, even if we had, we'd have to have some indexing/lookup mechanism atop the data). I didn't feel like the paper's response to this was all that convincing. It basically just argues that planning with model transitions can theoretically diverge (though acknowledges it empirically often doesn't), and that it's dangerous to update off of "fictional" modeled transitions that aren't grounded in real data. While it's obviously definitionally true that model transitions are in some sense fictional, that's just the basic trade-off of how modeling works: some ability to extrapolate, but a realization that there's a risk you extrapolate poorly. 

https://i.imgur.com/8jp22M3.png

The paper's empirical contribution to its argument was to argue that in a low-data setting, model-free RL (in the form of the "everything but the kitchen sink" Rainbow RL algorithm) with experience replay can outperform a model-based SimPLe system on Atari. This strikes me as fairly weak support for the paper's overall claim, especially since historically Atari has been difficult to learn good models of when they're learnt in actual-observation pixel space. Nonetheless, I think this push against the utility of model-based learning is a useful thing to consider if you do think models are useful, because it will help clarify the reasons why you think that's the case.

Originally posted [here](https://github.com/abhshkdz/papers/blob/master/reviews/actions-~-transformations.md).

This paper introduces a novel representation for actions in videos as transformations that change the state of the environment from what it was before the action (precondition) to what it will be after it (effect).

- Model
    - The model utilizes a Siamese architecture with each head having convolutional and fully-connected layers (similar to VGG16). Each head extracts features for a subset of video frames (precondition or effect) that are aggregated by average pooling and followed by a fully-connected layer.
    - The precondition frames are indexed from 1 to z\_p and the effect frames from z\_e to t. Both z\_p and z\_e are latent variables, constrained to be from [1/3t, 1/2t] and [1/2t, 2/3t] respectively and estimated via brute force search during training.
    - The action is represented as a linear transformation between the final fully-connected layers of the two heads. For n action categories, the transformation layer has n transformation matrices.
    - The model is trained with a contrastive loss function to 1) maximize cosine similarity between the effect embedding and the transformed precondition embedding, and 2) maximize distance for incorrect transformations if greater than a chosen margin.
- ACT Dataset
    - 50 keywords, 43 classes, ~500 YouTube videos per keyword.
    - The authors collect the ACT dataset primarily for the task of cross-category generalization (as it doesn't allow models to overfit to contextual information). For example, how would a model learned on "opening a window" generalize to recognize "opening the trunk of the car"? How about generalizing from a model trained on "climbing a cliff" to recognize "climbing a tree"?
    - The ACT dataset has class and super-class annotations from human workers. Each super-class has different sub-categories which are the same action under different subjects, objects and scenes.
- Experiments
    - Action recognition on UCF101, HMDB51, ACT.
    - Cross-category generalization on ACT.
- Visualizations
    - Nearest neighbor: modeling the actions as transformations gives semantically meaningful retrievals that don't just depend on motion and color.
    - Gradient visualizations (Simonyan et al. 2014): model focuses on changes in scene (human + object) than context.
    - Embedding retrievals based on transformed precondition embeddings.

** Thoughts **

- Modeling action as a transformation from precondition to effect is a very neat idea.
- The exact formulation and supporting experiments and ablation studies are thorough.
- During inference, the model first extracts features for all frames and then does a brute force search over (y,z\_p,z\_e) to estimate the action category and segmentation into precondition and effect. For longer sequences, this seems expensive. Although hard decisions aren't differentiable, a soft attention mechanism on z might be feasible and reduce computation to a single forward pass.

Rozsa et al. describe an adersarial attack against OpenMax [1] by directly targeting the logits. Specifically, they assume a network using OpenMax instead of a SoftMax layer to compute the final class probabilities. OpenMax allows “open-set” networks by also allowing to reject input samples. By directly targeting the logits of the trained network, i.e. iteratively pushing the logits in a target direction, it does not matter whether SoftMax or OpenMax layers are used on top, the network can be fooled in both cases.

Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/).

Gowal et al. propose interval bound propagation to obtain certified robustness against adversarial examples. In particular, given a neural network consisting of linear layers and monotonic increasing activation functions, a set of allowed perturbations is propagated to obtain upper and lower bounds at each layer. These lead to bounds on the logits of the network; these are used to verify whether the network changes its prediction on the allowed perturbations. Specifically, Gowal et al. consider an $L_\infty$ ball around input examples; the initial bounds are, thus, $\underline{z}_0 = x - \epsilon$ and $\overline{z}_0 = x + \epsilon$. For each layer, the bounds are defined as

$\underline{z}_{k,i} = \min_{\underline{z}_{k – 1} \leq z_{k – 1} \leq \overline{z}_{k-1}} e_i^T h_k(z_{k – 1})$

and the analogous maximization problem for the upper bound; here, $h$ denotes the applied layer. For Linear layers and monotonic activation functions, this is easy to solve, as shown in the paper. Moreover, computing these bounds is very efficient, only needing roughly two times the computation of one forward pass. During training, a combination of a clean loss and adversarial loss is used:

$\kappa l(z_K, y) + (1 - \kappa) l(\hat{z}_K, y)$

where $z_K$ are the logits of the input $x$, and $\hat{z}_K$ are the adversarial logits computed as

$\hat{Z}_{K,y’} = \begin{cases} \overline{z}_{K,y’} & \text{if } y’ \neq y\\\underline{z}_{K,y} & \text{otherwise}\end{cases}$

Both $\epsilon$ and $\kappa$ are annealed during training. In experiments, it is shown that this method results in quite tight bounds on robustness.

Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/).

Interacting with the environment comes sometimes at a high cost, for example in high stake scenarios like health care or teaching. Thus instead of learning online, we might want to learn from a fixed buffer $B$ of transitions, which is filled in advance from a behavior policy.
The authors show that several so called off-policy algorithms, like DQN and DDPG fail dramatically in this pure off-policy setting. 

They attribute this to the extrapolation error, which occurs in the update of a value estimate $Q(s,a)$, where the target policy selects an unfamiliar action $\pi(s')$ such that $(s', \pi(s'))$ is unlikely or not present in $B$. Extrapolation error is caused by the mismatch between the true state-action visitation distribution of the current policy and the state-action distribution in $B$ due to:
- state-action pairs (s,a) missing  in $B$, resulting in arbitrarily bad estimates of $Q_{\theta}(s, a)$ without sufficient data close to (s,a). 
- the finiteness of the batch of transition tuples $B$, leading to a biased estimate of the transition dynamics in the Bellman operator $T^{\pi}Q(s,a) \approx \mathbb{E}_{\boldsymbol{s' \sim B}}\left[r + \gamma Q(s', \pi(s')) \right]$
- transitions are sampled uniformly from $B$, resulting in a loss weighted w.r.t the frequency of data in the batch: $\frac{1}{\vert B \vert} \sum_{\boldsymbol{(s, a, r, s') \sim B}} \Vert r + \gamma Q(s', \pi(s')) - Q(s, a)\Vert^2$

The proposed algorithm Batch-Constrained deep Q-learning (BCQ) aims to choose actions that:
 1. minimize distance of taken actions to actions in the batch
 2. lead to states contained in the buffer
 3.  maximizes the value function,

where 1. is prioritized over the other two goals to mitigate the extrapolation error. 

Their proposed algorithm (for continuous environments) consists informally of the following steps that are repeated at each time $t$:
 1. update generator model of the state conditional marginal likelihood $P_B^G(a \vert s)$
 2. sample n actions form the generator model
 3. perturb each of the sampled actions to lie in a range $\left[-\Phi, \Phi \right]$
 4. act according to the argmax of respective Q-values of perturbed actions
 5. update value function

The experiments considers Mujoco tasks with four scenarios of batch data creation:
 - 1 million time steps from training a DDPG agent with exploration noise $\mathcal{N}(0,0.5)$ added to the action.This aims for a diverse set of states and actions. 
 - 1 million time steps from training a DDPG agent with an exploration noise $\mathcal{N}(0,0.1)$ added to the actions as behavior policy. The batch-RL agent and the behavior DDPG are trained concurrently from the same buffer. 
 - 1 million transitions from rolling out a already trained DDPG agent
 - 100k transitions from a behavior policy that acts with probability 0.3 randomly and follows otherwise an expert demonstration with added exploration noise  $\mathcal{N}(0,0.3)$

I like the fourth choice of behavior policy the most as this captures high stake scenarios like education or medicine the closest, in which training data would be acquired by human experts that are by the nature of humans not optimal but significantly better than learning from scratch. 

The proposed BCQ algorithm is the only algorithm that is successful across all experiments. It matches or outperforms the behavior policy. Evaluation of the value estimates showcases unstable and diverging value estimates for all algorithms but BCQ that exhibits a stable value function. 

The paper outlines a very important issue that needs to be tackled in order to use reinforcement learning in real world applications.