It is a fact universally acknowledged that a reinforcement learning algorithm not in possession of a model must be in want of more data. Because they generally are. Joking aside, it is broadly understood that model-free RL takes a lot of data to train, and, even when you can design them to use off-policy trajectories, collecting data in the real environment might still be too costly. Under those conditions, we might want to learn a model of the environment and generate synthesized trajectories, and train on those. This has the advantage of not needing us to run the actual environment, but the obvious disadvantage that any model will be a simplification of the true environment, and potentially an inaccurate one. These authors seek to answer the question of: “is there a way to generate trajectories that has higher fidelity to the true environment.” As you might infer from the fact that they published a paper, and that I’m now writing about it, they argue that, yes, there is, and it’s through explicit causal/counterfactual modeling. 

Causal modeling is one of those areas of statistics that seems straightforward at its highest level of abstraction, but tends to get mathematically messy and unintuitive when you dive into the math. So, rather than starting with equations, I’m going to try to verbally give some intuitions for the way causal modeling is framed here. Imagine you’re trying to understand what would happen if a person had gone to college. There’s some set of information you know about them, and some set of information you don’t, that’s just random true facts about them and about the universe. If, in the real world, they did go to college, and you want to simulate what would have happened if they didn’t, it’s not enough to just know the observed facts about them, you want to actually isolate all of the random other facts (about them, about the world) that weren’t specifically “the choice to go to college”, and condition on those as well. Obviously, in the example given here, it isn’t really practically possible to isolate all the specific unseen factors that influence someone’s outcome. But, conceptually, this quantity, is what we’re going to focus on in this paper. 

Now, imagine a situation where a RL agent has been dropped into a maze-like puzzle. It has some set of dynamics, not immediately visible to the player, that make it difficult, but ultimately solvable.  The best kind of simulated data, the paper argues, would be to keep that state of the world (which is partially unobservable) fixed, and sample different sets of actions the agent might take in that space. Thus, “counterfactual modeling”: for a given configuration of random states in the world, sampling different actions within it. To do this, you first have to infer the random state the agent is experiencing. In the normal model-based case, you’d have some prior over world states, and just sample from it. However, if you use the experience of the agent’s trajectory, you can make a better guess as to what world configuration it was dropped into. If you can do this, which is, technically speaking, sampling from the posterior over unseen context, conditional on an agent’s experience, then the paper suggests you’ll be able to generate data that’s more realistic, because the trajectories will be direct counterfactuals of “real world” scenarios, rather than potentially-unsolvable or unrealistic draws from the prior. 

This is, essentially, the approach proposed by the paper: during training, they make this “world state” visible to the agent, and let it learn a model predicting what state it started with, given some trajectory of experience. They also learn a model that predicts the outcome and ultimately the value of actions taken, conditioned on this random context (as well as visible context, and the agent’s prior actions). They start out by using this as a tool for policy evaluation, which is a nice problem setup because you can actually check how well you’re doing against some baseline: if you want to know how good your simulated data is at replicating the policy reward on real data, you can just try it out on real data and see. The authors find that they reduce policy reward estimation error pretty substantially by adding steps of experience (in Bayesian terms, bit of evidence moving them from the prior, towards the posterior). 

https://i.imgur.com/sNAcGjZ.png
They also experiment with using this for actual policy search, but, honestly, I didn’t quite follow the intuitions behind Guided Policy Search, so I’m just going to not dive into that for now, since I think a lot of the key contributions of the paper are wrapped up in the idea of “estimate the reward of a policy by simulating data from a counterfactual trajectory”

How can humans help an agent perform at a task that has no clear reward? Imitation, demonstration, and preferences. This paper asks which combinations of imitation, demonstration, and preferences will best guide an agent in Atari games.

For example an agent that is playing Pong on the Atari, but can't access the score. You might help it by demonstrating your play style for a few hours. To help the agent further you are shown two short clips of it playing and you are asked to indicate which one, if any, you prefer.

To avoid spending many hours rating videos the authors sometimes used an automated approach where the game's score decides which clip is preferred, but they also compared this approach to human preferences. It turns out that human preferences are often worse because of reward traps. These happen, for example, when the human tries to encourage the agent to explore ladders, resulting in the agent obsessing about ladders instead of continuing the game.

They also observed that the agent often misunderstood the preferences it was given, causing unexpected behavior called reward hacking. The only solution they mention was to have someone keep an eye on it and continue giving it preferences, but this isn't always feasible. This is the alignment problem which is a hard problem in AGI research.

Results: adding merely a few thousand preferences can help in most games, unless they have sparse rewards. Demonstrations, on the other hand, tend to help those games with sparse rewards but only if the demonstrator is good at the game.

This paper feels a bit like watching a 90’s show, and everyone’s in denim and miniskirts, except it’s a 2017 ML paper, and everything uses attention. (I’ll say it again, ML years are like dog years, but more so). That said, that’s not a critique of the paper: finding clever ways to cobble together techniques for your application can be an important and valuable contribution. This paper addresses the problem of text to image generation: how to take a description of an image and generate an image that matches it, and it makes two main contributions: 1) a GAN structure that seems to merge insights from Attention and Progressive GANs in order to select areas of the sentence to inform details in specific image regions, and 2) a novel discriminator structure to evaluate whether a sentence matches an image. 

https://i.imgur.com/JLuuhJF.png

Focusing on the first of these first: their generation system works by an iterative process, that gradually builds up image resolution, and also pulls specific information from the sentence to inform details in each region. The first layer of the network generates a first “hidden state” based on a compressed representation of the sentence as a whole (the final hidden state of a LSTM text encoder, I believe), as well as random noise (typical input to a GAN). Subsequent “hidden states” are calculated by calculating attention weightings between each region of the image, and each word in the sentence, and pulling together a per-region context vector based on that attention map. (As far as I understand it, “region” here refers to the fact that when you’re at lower spatial scales of what is essentially a progressive generation process, 64x64 rather than 256x256, for example, each “pixel” actually represents a larger region of the image). I’m using quotes around “hidden state” in the above paragraph because I think it’s actually pretty confusing terminology, since it suggests a recurrent structure, but this model isn’t actually recurrent: there’s a specific set of weights for resolution block 0, and 1, and 2. This whole approach, of calculating a specific attention-weighted context vector over input words based on where you are in the generation process is very conceptually similar to the original domain of attention, where the attention query would be driven by the hidden state of the LSTM generating the translated version of some input sentence, except, here, instead of translating between languages, you’re translating across mediums. 

The loss for this model is a combination of per-layer loss, and a final, special, full-resolution loss. At each level of resolution, there exists a separate discriminator, which seems to be able to take in both 1) only an image, and judge whether it thinks that image looks realistic on it’s own, and 2) an image and a global sentence vector, and judge whether the image matches the sentence. It’s not fully clear from the paper, but it seems like this is based on just feeding in the sentence vector as additional input? 
https://i.imgur.com/B6qPFax.png
For each non-final layer’s discriminator, the loss is a combination of both of these unconditional and conditional losses. 

The final contribution of this paper is something they call the DAMSM loss: the Deep Attention Multimodal Similarity Model. This is a fairly complex model structure, whose ultimate goal is to assess how closely a final generated image matches a sentence. The whole structure of this loss is based on projecting region-level image features (from an intermediate, 17x17 layer of a pretrained Inception Net) and word features into the same space, and then calculating dot product similarities between them, which are then used to build “visual context vectors” for each word (for each word, created a weighted sum of visual vectors, based on how similar each is to the word). Then, we take each word’s context vector, and see how close it is to the original word vector. If we, again, imagine image and word vectors as being in a conceptually shared space, then this is basically saying “if I take a weighted average of all the things that are the most similar to me, how ultimately similar is that weighted average to me”. This allows there to be a “concept representation” match found when, for example, a particular word’s concept, like “beak”, is only present in one region, but present there very strongly: the context vector will be strongly weighted towards that region, and will end up being very close, in cosine similarity terms, to the word itself. By contrast, if none of the regions are a particularly good match for the word’s concept, this value will be low. DAMSM then aggregates up to an overall “relevance” score between a sentence and image, that’s simply a sum over a word’s “concept representation”, for each word in a sentence. It then calculates conditional probabilities in two directions: what’s the probability of the sentence, given the image (relevance score of (Sent, Imag), divided by that image’s summed relevance with all possible sentences in the batch), and, also, what’s the probability of the image, given the sentence (relevance score of the pair, divided by the sentence’s summed relevance with all possible images in the batch). 

In addition to this word-level concept modeling, DAMSM also has full sentence-level versions, where it simply calculates the relevance of each (sentence, image) pair by taking the cosine similarity between the global sentence and global image features (the final hidden state of an encoder RNN, and the final aggregated InceptionNet features, respectively). All these losses are aggregated together, to get one that uses both global information, and information as to whether specific words in a sentence are represented well in an image. 

This is a paper where I keep being torn between the response of “this is so simple it’s brilliant; why haven’t people done it before,” and “this is so simple it’s almost tautological, and the results I’m seeing aren’t actually that surprising”. The basic observation this paper makes is one made frequently before, most recently to my memory by Geoff Hinton in his Capsule Net paper: sometimes the translation invariance of convolutional networks can be a bad thing, and lead to worse performance. In a lot of ways, translation invariance is one of the benefits of using a convolutional architecture in the first place: instead of having to learn separate feature detectors for “a frog in this corner” and “a frog in that corner,” we can instead use the same feature detector, and just move it over different areas of the image. However, this paper argues, this makes convolutional networks perform worse than might naively be expected at tasks that require them to remember or act in accordance with coordinates of elements within an image. 

For example, they find that normal convolutional networks take nearly an hour and 200K worth of parameters to learn to “predict” the one-hot encoding of a pixel, when given the (x,y) coordinates of that pixel as input, and only get up to about 80% accuracy. Similarly, trying to take an input image with only one pixel active, and predict the (x,y) coordinates as output, is something the network is able to do successfully, but only when the test points are sampled from the same spatial region as the training points: if the test points are from a held-out quadrant, the model can’t extrapolate to the (x, y) coordinates there, and totally falls apart. 

https://i.imgur.com/x6phN4p.png

The solution proposed by the authors is a really simple one: at one or more layers within the network, in addition to the feature channels sent up from the prior layer, add two addition channels: one with a with deterministic values going from -1 (left) to 1 (right), and the other going top to bottom. This essentially adds two fixed “features” to each pixel, which jointly carry information about where it is in space. Just by adding this small change, we give the network the ability to use spatial information or not, as it sees fit. If these features don’t prove useful, their weights will stay around their initialization values of expectation-zero, and the behavior should be much like a normal convolutional net. However, if it proves useful, convolution filters at the next layer can take position information into account. It’s easy to see how this would be useful for this paper’s toy problems: you can just create a feature detector for “if this pixel is active, pass forward information about it’s spatial position,” and predict the (x, y) coordinates out easily. You can also imagine this capability helping with more typical image classification problems, by having feature filters that carry with them not only content information, but information about where a pattern was found spatially.  

The authors do indeed find comparable performance or small benefits to ImageNet, MNIST, and Atari RL, when applying their layers in lieu of normal convolutional layer. On GANs in particular, they find less mode collapse, though I don’t yet 100% follow the intuition of why this would be the case. 
https://i.imgur.com/wu7wQZr.png

This paper was a real delight to read, and even though I’m summarizing it here, I’d really encourage you, if you’re reading this, to read the paper itself, since I found it to be unusually clearly written. It tackles the problem of understanding how features of loss functions - these integral, yet arcane, objects defined in millions of parameter-dimensions - impact model performance. Loss function analysis is generally a difficult area, since the number of dimensions and number of points needed to evaluate to calculate loss are both so high. The latter presents computational challenges, the former ones of understanding: human brains and many-dimensional spaces are not a good fit. Overall, this paper contributes by 1) arguing for a new way of visualizing loss functions, 2) demonstrating how and in what cases “flatness” of loss function contributes to performance and trainability, and 3)) 

The authors review a few historically common ways of visualizing loss functions, before introducing their variant. The simplest, one-dimensional visualization technique, 1-D Linear Interpolation, works by taking two parameter settings (say, a random initialization, and the final network minimum), and smoothly interpolating between the two, by taking a convex combination mediated by alpha. Then, you can plot the value of the loss at all of these parameter configurations as a function of alpha. If you want to plot in 2D, with a contour plot, you can do so in a pretty similar manner, by picking two random “direction vectors” of the same size as the parameter vector, and then adding amounts of those directions, weighted by alpha and beta, to your starting point. These random directions become your axes, and you get a snapshot of the change in your loss function as you move along them. 


The authors then make the observation that these techniques can’t natively be used to compare two different models, if the parameters of those models are on different scales. If you take a neural net, multiply one layer by 10, and then divide the next layer by 10, you’ve essentially done a no-op that won’t impact the outcome. However, if you’re moving by a fixed amount along your random direction in parameter space, you’ll have to move much farther to go the commensurate amount of distance in the network that’s been multiplied by 10. To address this problem, they suggest a simple fix: after you’ve selected each of your random directions, scale the value in each direction vector by the norm of the filter that corresponds to that value. This gets rid of the sensitivity of your plots to the scale of weights. (One thing I admit I’m a little confused by here is the fact that each value in the direction vector corresponds to a filter, rather than to a weight; I would have natively thought theta, and all the direction vectors, are of length number-of-model-parameters, and each value is a single weight. I think I still broadly grasp the intuition, but I’d value having a better sense of this). 

To demonstrate the value of their normalization system, they compare the interpolation plots for a model with small and large batch size, with and without weight decay. Small batches are known to increase flatness of the loss function around the eventual minimum, which seems co-occurrent with good generalization results. And, that bears out in the original model’s linear interpolation (figs a, b, c), where the small model has the wider solution basin, and also better performance. However, once weight decay is applied (figs d, e, f), the small-batch basin appears to shrink to be very narrow, although small-batch still has dominant performance. At first glance, this would seem to be a contradiction of the “flatter solutions mean more generalization” rule.  

https://i.imgur.com/V0H13kK.png

But this is just because weight decay hits smaller models more strongly, because they have more distinct updates during which they apply the weight decay penalty. This means that when weight decay is applied, the overall scale of weights in the small-batch network is lower, and so it’s solution looked “sharp” when plotted on the same weight scale as the large-batch network. When normalization was used, this effect by and large went away, and you once again saw higher performance with flatter loss functions. (batch size and performance with and without weight decay, shown normalized below)

https://i.imgur.com/vEUIgo0.png

A few other, more scattered observations from the paper:

- I’ve heard explanations of skip connections in terms of “giving the model shorter gradient paths between parameters and output,” but haven’t really seen an argument for why skip connections lead to smoother loss functions, even they empirically seem to

https://i.imgur.com/g3QqRzh.png

- The authors also devise a technique for visualizing the change in loss function along the trajectory taken by the optimization algorithm, so that different ones can be compared.  The main problem in previous methods for this has been that optimization trajectories happen in a low-dimensional manifold within parameter space, so if you just randomly select directions, you won’t see any interesting movement along the trajectory. To fix this, they choose as their axes the principal components you get from making a matrix out of the parameter values at each epoch: this prioritizes the parameters that had the most variance throughout training.