ot sufficient to simply choose a fixed penalty coefficient β and optimize the penalizedobjective Equation (5) with SGD

objective function (the “surrogate” objective) is maximized

Generalizingthis choice, we can use a truncated version of generalized advantage estimation

Without a constraint, maximization of LCP I would lead to an excessively large policyupdate; hence, we now consider how to modify the objective, to penalize changes to the policy thatmove rt(θ) away from 1

our goalof a first-order algorithm that emulates the monotonic improvement of TRPO,

A proximal policy optimization (PPO) algorithm that uses fixed-length trajectory segments isshown below. Each iteration, each of N (parallel) actors collect T timesteps of data. Then weconstruct the surrogate loss on these N T timesteps of data, and optimize it with minibatch SGD

Thefirst term inside the min is LCP I . The second term, clip(rt(θ), 1 − , 1 + ) ˆAt, modifies the surrogateobjective by clipping the probability ratio, which removes the incentive for moving rt outside of theinterval [1 − , 1 + ]. Finally, we take the minimum of the clipped and unclipped objective, so thefinal objective is a lower bound (i.e., a pessimistic bound) on the unclipped objective

Clipped Surrogate Objective

Wecan see that LCLIP is a lower bound on LCP I , with a penalty for having too large of a policyupdate

hese methods havethe stability and reliability of trust-region methods but are much simpler to implement, requiringonly few lines of code change to a vanilla policy gradient implementation, applicable in more generalsetting

shows howseveral objectives vary as we interpolate along the policy update direction

Surrogate objectives, as we interpolate between the initial policy parameter θold, and the updatedpolicy parameter, which we compute after one iteration of PPO.

lower bound (i.e., a pessimistic bound

The theory justifying TRPO actually suggests using a penalty instead of a constraint, i.e.,solving the unconstrained optimization problemmaximizeθˆEt[ πθ(at | st)πθold (at | st) ˆAt − β KL[πθold (· | st), πθ(· | st)]](5)for some coefficient β

New transitions

bias towards re-cent transitions

samples transitions with probability ptrelative to the last encountered absolute TD error

RMSprop

his means thatin the loss above, the time index t will be a random time in-dex from the last million transitions, rather than the currenttime.

Multi-step learning.

Prioritized replay.

Prioritized

parameters θ of the online network (which is alsoused to select actions

ablation

θ represents the parame-ters of a target network

a periodic copy of the online net-work which is not directly optimized.

Noisy Nets. The limitations of exploring using -greedypolicies are clear in games such as Montezuma’s Revenge,where many actions must be executed to collect the first re-ward

t is a time step randomly picked from the replaymemory

DDQN

This means that the target values are constrained to change slowly, greatlyimproving the stability of learning.

A major challenge of learning in continuous action spaces is exploration. An advantage of off-policies algorithms such as DDPG is that we can treat the problem of exploration independentlyfrom the learning algorithm.

but modified for actor-critic and using “soft” target updates, rather thandirectly copying the weights.

his simple change moves the relatively unstable problem oflearning the action-value function closer to the case of supervised learning, a problem for whichrobust solutions exist.

One approach to this problem is to manually scale the features so they are in similar ranges acrossenvironments and units. We address this issue by adapting a recent technique from deep learningcalled batch normalization

minimize covariance shif

normalizes each dimensionacross the samples in a minibatch to have unit mean and variance

For many tasks our models exhibit human-level performance, and we are the first to report computer agents that can craftdiamond tools, which can take proficient humans upwards of 20 minutes (24,000environment actions) of gameplay to accomplish

e extend the internet-scalepretraining paradigm to sequential decision domains through semi-supervisedimitation learning wherein agents learn to act by watching online unlabeled videos.

an agent isinstructed to obtain a desired goal item

urriculum learning (at least using current RL methods) is that the agentachieves a small success probability (within available/reasonable compute) on a new task aftermastering a previous task.

We study curriculum learning on a set of goal-conditioned Minecraft tasks, in which the agent istasked to collect one out of a set of 107 items from the Minecraft tech tree

Results

It has 5 minutes (1500 time steps) to complete the task and obtains areward of +1 upon success. After each success or failure a new task is selected without resettingthe world or respawning the agent

Simon Says”

Learning progress curriculum

Few-Shot (FS) - the model is given a few demonstrations of the task at inference time asconditioning [ RWC+19 ], but no weights are updated

fuzzy

[KMH+20] Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B. Brown, Benjamin Chess,Rewon Child, Scott Gray, Alec Ra

As found in [ KMH+20 , MKAT18 ], larger models can typically use a larger batch size, but requirea smaller learning rate. We measure the gradient noise scale during training and use it to guideour choice of batch size [MKAT18 ]. Table A.1 shows the parameter settings we used. To train thelarger models without running out of memory, we use a mixture of model parallelism within eachmatrix multiply and model parallelism across the layers of the network. All models were trained onV100 GPU’s on part of a high-bandwidth cluster. Details of the training process and hyperparametersettings are described in the appendix.

We use the same model and architecture as GPT-2

While zero-shot performance establishes a baseline of thepotential performance of GPT-2 on many tasks, it is notclear where the ceiling is with finetuning.

13.19%

The Bloom filterswere constructed such that the false positive rate is upperbounded by 1108 . We further verified the low false positiverate by generating 1M strings, of which zero were found bythe filter

Bloom filters

Recent work in computer vision has shown that common im-age datasets contain a non-trivial amount of near-duplicateimages. For instance CIFAR-10 has 3.3% overlap betweentrain and test images (Barz & Denzler, 2019). This results inan over-reporting of the generalization performance of ma-chine learning systems.

e also add 8,000 text-instructions generated bythe OpenAI API gpt-3.5-turbo model [38],

introducing a unified framework that converts all text-basedlanguage problems into a text-to-text format

In this way, an NTM can be thought of as simultaneously exploring all computational possibilities in parallel and selecting an accepting branch

Computational problems[edit] Intuitively, a computational problem is just a question that can be solved by an algorithm. For example, "is the natural number n {\displaystyle n} prime?" is a computational problem. A computational problem is mathematically represented as the set of answers to the problem. In the primality example, the problem (call it PRIME {\displaystyle {\texttt {PRIME}}} ) is represented by the set of all natural numbers that are prime: PRIME = { n ∈ N | n  is prime } {\displaystyle {\texttt {PRIME}}=\{n\in \mathbb {N} |n{\text{ is prime}}\}} . In the theory of computation, these answers are represented as strings; for example, in the primality example the natural numbers could be represented as strings of bits that represent binary numbers. For this reason, computational problems are often synonymously referred to as languages, since strings of bits represent formal languages (a concept borrowed from linguistics); for example, saying that the PRIME {\displaystyle {\texttt {PRIME}}} problem is in the complexity class NP is equivalent to saying that the language PRIME {\displaystyle {\texttt {PRIME}}} is in NP.

Presburger arithmetic is much weaker than Peano arithmetic, which includes both addition and multiplication operations. Unlike Peano arithmetic, Presburger arithmetic is a decidable theory. This means it is possible to algorithmically determine, for any sentence in the language of Presburger arithmetic, whether that sentence is provable from the axioms of Presburger arithmetic. The asymptotic running-time computational complexity of this algorithm is at least doubly exponential, however, as shown by Fischer & Rabin (1974).

NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP

At present, all known algorithms for NP-complete problems require time that is superpolynomial in the input size, in fact exponential in O ( n k ) {\displaystyle O(n^{k})} [clarify] for some k > 0 {\displaystyle k>0} and it is unknown whether there are any faster algorithms.

The Subgraph Isomorphism problem is NP-complete. The graph isomorphism problem is suspected to be neither in P nor NP-complete, though it is in NP. This is an example of a problem that is thought to be hard, but is not thought to be NP-complete. This class is called NP-Intermediate problems and exists if and only if P≠NP.

NP-complete problems are often addressed by using heuristic methods and approximation algorithms.

GPT-4 outperforms ChatGPT by scoring in higher approximate percentiles among test-takers.

40% more likely to produce factual responses than GPT-3.5

We used GPT-4 to help create training data for model fine-tuning and iterate on classifiers across training, evaluations, and monitoring.

"There is a robust debate going on in the computing industry about how to create it, and whether it can even be created at all."

asks for the Minecraft domain.

Definition 3.2 (simple reward machine).

e thenshow that an RM can be interpreted as specifying a single reward function over a largerstate space, and consider types of reward functions that can be expressed using RMs

However, an agent that hadaccess to the specification of the reward function might be able to use such information tolearn optimal policies faster.

U is a finite set of states,

state-reward function,

Reward Machines: Exploiting Reward FunctionStructure in Reinforcement Learning

Using Reward Machines for High-Level Task Specificationand Decomposition in Reinforcement Learning

Bell’s theorem is aboutcorrelations (joint probabilities) of stochastic real variables and therefore doesnot apply to quantum theory, which neither describes stochastic motion nor usesreal-valued observables

make up facts less often

On prompts submitted by our customers to the API,[1

10K

n embedding for each timestep is learned and added to eachtoken – note this is different than the standard positional embedding used by transformers, as onetimestep corresponds to three tokens

we propose the Transformer, a model architecture eschewing recurrence and insteadrelying entirely on an attention mechanism to draw global dependencies between input and output.The Transformer allows for significantly more parallelization a

We study whether sequence modelingcan perform policy optimization by evaluating Decision Transformer on offline RL benchmarks

As a baseline model we took the feature representation from a large pre-trained CNN such as ResNet50, by using the model and excluding the final dense layer, and using this in place of our convolution layers. We had predicted that this would likely get us some performance, but would inherently be worse, since we had fixed some of our trainable parameters.

Weak supervision also objectively identifies relevant morphological features from the tissue microenv-iornment without any a priori knowledge or subjective annotation. In three separate analyses, we showed thatour models can identify well-known morphological features and accordingly, has the capability of identify-ing new morphological features of diagnostic, prognostic, and therapeutic relevance.

The Canadian experiment has been built, in large part, around the American experiment: They have the melting pot, we have the cultural mosaic; they have the free market, we have sensible regulation; they have “life, liberty and the pursuit of happiness,” we have “peace, order and good government.”

Northrop Frye once defined a Canadian as “an American who rejects the Revolution.”

A flaw lurked right at the core of the experiment, as flaws so often do in works of ambitious genius.

Difference is the core of the American experience. Difference is its genius. There has never been a country so comfortable with difference, so full of difference.

Such a map, plus the universal property of AA A<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math>, is in fact enough to reconstruct the entire Turing structure of CC \mathsf{C}<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mstyle mathvariant="sans-serif"><mi>C</mi></mstyle></mrow><annotation encoding="application/x-tex">\mathsf{C}</annotation></semantics></math>.

not necessarily extensional, only intensional)