Do you want BuboFlash to help you learning these things? Click here to log in or create user.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#computer-science #machine-learning #reinforcement-learning

Among the algorithms investigated so far in this book, only the Monte Carlo methods are true SGD methods. These methods converge robustly under both on-policy and off-policy training as well as for general nonlinear (differentiable) function approximators, though they are often slower than semi-gradient methods with bootstrapping, which are not SGD methods.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#reinforcement-learning

We consider a broader class of Bellman equations that are non-linear in the rewards and future values: \(v(s)=\mathbb{E}\left[f\left(R_{t+1}, v\left(S_{t+1}\right)\right) | S_{t}=s, A_{t} \sim \pi\left(S_{t}\right)\right]\) .

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#reinforcement-learning

Humans and animals seem to exhibit a different type of weighting of the future than would emerge from the standard linear Bellman equation which leads to exponential discounting when unrolled multiple steps because of the repeated multiplication with γ . One consequence is that the preference ordering of two dif- ferent rewards occurring at different times can reverse, depending on how far in the future the first reward is. For instance, humans may prefer a single sparse reward of + 1 (e.g., $1) now over a reward of + 2 (e.g., $2) received a week later, but may also prefer a re- ward of + 2 received after 20 weeks over a reward of + 1 after 19 weeks.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#reinforcement-learning

As mentioned in the introduction, in this paper we are interested in the multitask RL scenario, where the agent has to solve multiple tasks. Each task is defined by a reward function R w ; thus, instead of a single MDP M , our environment is a set of MDPs that share the same structure except for the reward function. Following Barreto et al. (2017), we assume that the expected one-step reward associated with transition \(s \stackrel{a}{\rightarrow} s^{\prime}\) is given by \(\mathrm{E}\left[R_{\mathbf{w}}\left(s, a, s^{\prime}\right)\right]=r_{\mathbf{w}}\left(s, a, s^{\prime}\right)=\phi\left(s, a, s^{\prime}\right)^{\top} \mathbf{w}\), where \(\phi\left(s, a, s^{\prime}\right) \in \mathbb{R}^{d}\) are features of (s, a, s') and \(\mathbf{w} \in \mathbb{R}^{d}\) are weights.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#reinforcement-learning

SFs allow one to immediately compute the value of a policy π on any task w : it is easy to show that, when (1) holds, Q π w (s, a) = ψ π (s, a) > w . It is also easy to see that SFs satisfy a Bellman equation in which φ play the role of rewards, so ψ can be learned using any RL method (Szepesv ´ ari, 2010).

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#reinforcement-learning

As one can see, the types of generalisation provided by UVFAs and SF&GPI are in some sense complementary. It is then natural to ask if we can simultaneously have the two types of generalisation. In this paper we propose a model that provides exactly that. The main insight is actually simple: since SFs are multi-dimensional value functions, we can extend them in the same way as universal value functions extend regular value functions. In the next section we elaborate on how exactly to do so.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

The notion of convexity underlies a lot of beautiful mathematics. When combined with computation, it gives rise to the area of convex optimization that has had a huge impact on understanding and improving the world we live in. However, convexity does not provide all the answers. Many procedures in statistics, machine learning and nature at large—Bayesian inference, deep learning, protein folding—successfully solve non-convex problems that are NP-hard, i.e., intractable on worst-case instances. Moreover, often nature or humans choose methods that are inefficient in the worst case to solve problems in P.

Can we develop a theory to resolve this mismatch between reality and the predictions of worst-case analysis? Such a theory could identify structure in natural inputs that helps sidestep worst-case complexity.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

Off the Convex Path – Off the convex path About Contact Subscribe Off the Convex Path Contributors Sanjeev Arora Moritz Hardt Nisheeth Vishnoi Nadav Cohen Mission statement The notion of convexity underlies a lot of beautiful mathematics. When combined with computation, it gives rise to the area of convex optimization that has had a huge impact on understanding and improving the world we live in. However, convexity does not provide all the answers. Many procedures in statistics, machine learning and nature at large—Bayesian inference, deep learning, protein folding—successfully solve non-convex problems that are NP-hard, i.e., intractable on worst-case instances. Moreover, often nature or humans choose methods that are inefficient in the worst case to solve problems in P. Can we develop a theory to resolve this mismatch between reality and the predictions of worst-case analysis? Such a theory could identify structure in natural inputs that helps sidestep worst-case complexity. This blog is dedicated to the idea that optimization methods—whether created by humans or nature, whether convex or nonconvex—are exciting objects of study and, often lead to useful alg

This blog is dedicated to the idea that optimization methods—whether created by humans or nature, whether convex or nonconvex—are exciting objects of study and, often lead to useful algorithms and insights into nature. This study can be seen as an extension of classical mathematical fields such as dynamical systems and differential equations among others, but with the important addition of the notion of computational efficiency.

We will report on interesting research directions and open problems, and highlight progress that has been made. We will write articles ourselves as well as encourage others to contribute. In doing so, we hope to generate an active dialog between theorists, scientists and practitioners and to motivate a generation of young researchers to work on these important problems.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

a theory to resolve this mismatch between reality and the predictions of worst-case analysis? Such a theory could identify structure in natural inputs that helps sidestep worst-case complexity. <span>This blog is dedicated to the idea that optimization methods—whether created by humans or nature, whether convex or nonconvex—are exciting objects of study and, often lead to useful algorithms and insights into nature. This study can be seen as an extension of classical mathematical fields such as dynamical systems and differential equations among others, but with the important addition of the notion of computational efficiency. We will report on interesting research directions and open problems, and highlight progress that has been made. We will write articles ourselves as well as encourage others to contribute. In doing so, we hope to generate an active dialog between theorists, scientists and practitioners and to motivate a generation of young researchers to work on these important problems. Contributing an article If you’re writing an article for this blog, please follow these guidelines. Theme available on Github. sharedunsaved Last Modified: Close[x] R+ Annotation 436254

We are interested in understanding what end-to-end matrix W W emerges when we run GD on an LNN to minimize a general convex loss L ( W ) L(W) , and in particular the matrix completion loss given above. Note that L ( W ) L(W) is convex, but the objective obtained by over-parameterizing with an LNN is not. We analyze the trajectories of W W , and specifically the dynamics of its singular value decomposition. Denote the singular values by { σ r } r \{ \sigma_r \}_r , and the corresponding left and right singular vectors by { u r } r \{ \mathbf{u}_r \}_r and { v r } r \{ \mathbf{v}_r \}_r respectively.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

I finally got around to reading this new paper by Arjovsky et al. It debuted on Twitter with a big splash, being decribed as 'beautiful' and 'long awaited' 'gem of a paper'. It almost felt like a new superhero movie or Disney remake just came out.

- Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, David Lopez-Paz (2019) Invariant Risk Minimization

The paper is, indeed, very well written, and describes a very elegant idea, a practical algorithm, some theory and lots of discussion around how this is related to various bits. Here, I will describe the main idea and then provide an information theoretic view on the same topic.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

Invariant Risk Minimization: An Information Theoretic View inFERENCe posts on machine learning, statistics, opinions on things I'm reading in the space Home July 19, 2019 Invariant Risk Minimization: An Information Theoretic View I finally got around to reading this new paper by Arjovsky et al. It debuted on Twitter with a big splash, being decribed as 'beautiful' and 'long awaited' 'gem of a paper'. It almost felt like a new superhero movie or Disney remake just came out. Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, David Lopez-Paz (2019) Invariant Risk Minimization The paper is, indeed, very well written, and describes a very elegant idea, a practical algorithm, some theory and lots of discussion around how this is related to various bits. Here, I will describe the main idea and then provide an information theoretic view on the same topic. Summary of the approach We would like to learn robust predictors that are based on invariant causal associations between variables, rather than spurious surface correlations that might

#computer-science #machine-learning #reinforcement-learning

Thus, following the standard SGD approach, one can derive the per-step update based on a sample of this expected value: w t+1 = w t 1 2 ↵r(⇢ t 2 t ) = w t ↵⇢ t t r t = w t + ↵⇢ t t rˆv(S t ,w t ) rˆv(S t+1 ,w t ) , (11.23) which you will recognize as the same as the semi-gradient TD algorithm (11.2) except f or the additional final term.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#computer-science #machine-learning #reinforcement-learning

In the general function-approximation case, the one-step TD error with discounting is t = R t+1 + ˆv(S t+1 ,w t ) ˆv(S t ,w t ). A possible objective function then is what one might call the Mean Squared TD Error: TDE(w)= X s2S µ(s)E ⇥ 2 t S t =s, A t ⇠⇡ ⇤

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#computer-science #machine-learning #reinforcement-learning

The Bellman error for a stat e is the expected TD error in that state. So let’s repeat the d er i vation above with the expected TD error (all expectations here are implicitly conditional on S t ): w t+1 = w t 1 2 ↵r(E ⇡ [ t ] 2 ) = w t 1 2 ↵r(E b [⇢ t t ] 2 ) = w t ↵E b [⇢ t t ] rE b [⇢ t t ] = w t ↵E b ⇥ ⇢ t (R t+1 + ˆv(S t+1 ,w) ˆv(S t ,w)) ⇤ E b [⇢ t r t ] = w t + ↵ h E b ⇥ ⇢ t (R t+1 + ˆv(S t+1 ,w)) ⇤ ˆv(S t ,w) ih rˆv(S t ,w) E b ⇥ ⇢ t rˆv(S t+1 ,w) ⇤ i . This update and various ways of samp li n g it are referred to as the residual-gradient algorithm.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#computer-science #machine-learning #reinforcement-learning

But this is naive, because the equ at i on above involves t h e next state, S t+1 , appearing in two expectations that are multiplied together. To get an unbiased sample of the product, two independent samples of the next state are required, but during normal interaction with an external environment only one is obtaine d.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#computer-science #machine-learning #reinforcement-learning

In either of these cases t h e residual-gradient algorithm is guar anteed to converge to a minimum of t h e BE under the usual conditions on the step-size parameter.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#computer-science #machine-learning #reinforcement-learning

This example shows intuitively that minimizing th e BE (which the residual-gradient algorithm surely does) may not be a desirable goal.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#computer-science #machine-learning #reinforcement-learning

If an objective cannot b e learned, it does in de ed draw its utility into question. In the case of the VE , however, there is a way out. Note that the same solution, w = 1, is optimal for both MRPs above (assuming µ is the same for the two indistinguishable states in the right MRP). Is this a coincidence, or could it be generally t ru e that all MDPs with the same data distribution also have the same optimal parameter vector? If this is true—and we will show next that it is—then the VE remains a usable objective. The VE is not learnable, but the parameter that optimizes it is!

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#computer-science #machine-learning #reinforcement-learning

One error t h at is always observable is that between the value estimate at each time and the return from that time. The Mean Square Return Error, denoted RE , is the expectation, unde r µ , of the square of this error. In the on-policy case the RE can be written RE(w)=E h G t ˆv(S t ,w) 2 i = VE(w)+E h G t v ⇡ (S t ) 2 i . (11.24)

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#computer-science #machine-learning #reinforcement-learning

Thus, t he BE is not learnable; it cannot be estimated from featu r e vectors and other observable data. This limits the BE to model-based settings.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#computer-science #machine-learning #reinforcement-learning

Figure 11.4: Causal relationships amon g the data distrib u t i o n , MDPs, and various objectives. Left, Monte Carlo objectives: Two di↵erent MDPs can produce the same d a t a distribution yet also produce d i↵erent VE s, proving that t h e VE objective cannot be determined from data and is not learnable. However, all su ch VE s must have the same optimal parameter vector, w ⇤ ! Moreover, this same w ⇤ can be determined from another object ive, the RE ,whichis uniquely determined from the data distribution. Thus w ⇤ and the RE are learnable even though the VE s are not. Right, Bootstrapping objectives: Two di↵erent MDPs can produce the same data distribution yet al so produce di↵ere nt BE s and have di↵erent minimizing parameter vectors; these are not learn a b le from the data distribution. The PBE and TDE objectives and their (di↵erent) minima can be directly determined from data and thus are learnable.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#has-images #learning #machine #statistics

Machine learning From Wikipedia, the free encyclopedia Jump to navigationJump to search For the journal, see Machine Learning (journal). "Statistical learning" redirects here. For statistical learning in linguistics, see statistical learning in language acquisition. Machine learning and data mining Problems[show] Supervised learning (classification • regression) [show] Clustering[show] Dimensionality reduction[show] Structured prediction[show] Anomaly detection[show] Artificial neural networks[show] Reinforcement learning[show] Theory[show] Machine-learning venues[show] Glossary of artificial intelligence[show] Related articles[show] v t e Machine learning (ML) is the scientific study of algorithms and statistical models that computer systems use to perform a specific task without using explicit instructions, rely

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

Like a cat about to pounce, your body is prepared to spring into action with a burst of energy.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

we start worrying and try to exert too much conscious control over our playing.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

“You may not be able to stop the waves...but you can learn to surf.”

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

The 7 steps of “Centering”

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

you can hear Leon Fleisher talking about clear intentions in his own words.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

Progressive muscle relaxation (PMR)

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

#learning #machine #statistics

**Machine learning** (**ML**) is the scientific study of algorithms and statistical models that computer systems use to perform a specific task without using explicit instructions, relying on patterns and inference instead. It is seen as a subset of artificial intelligence. Machine learning algorithms build a mathematical model based on sample data, known as "training data", in order to make predictions or decisions without being explicitly programmed to perform the task.^{[1]}^{[2]}^{:2} Machine learning algorithms are used in a wide variety of applications, such as email filtering and computer vision, where it is difficult or infeasible to develop a conventional algorithm for effectively performing the task.

Machine learning is closely related to computational statistics, which focuses on making predictions using computers. The study of mathematical optimization delivers methods, theory and application domains to the field of machine learning. Data mining is a field of study within machine learning, and focuses on exploratory data analysis through unsupervised learning.^{[3]}^{[4]} In its application across business problems, machine learning is also referred to as predictive analytics.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

tection [show] Artificial neural networks [show] Reinforcement learning [show] Theory[show] Machine-learning venues[show] Glossary of artificial intelligence [show] Related articles[show] v t e <span>Machine learning (ML) is the scientific study of algorithms and statistical models that computer systems use to perform a specific task without using explicit instructions, relying on patterns and inference instead. It is seen as a subset of artificial intelligence . Machine learning algorithms build a mathematical model based on sample data, known as "training data ", in order to make predictions or decisions without being explicitly programmed to perform the task.[1] [2] :2 Machine learning algorithms are used in a wide variety of applications, such as email filtering and computer vision , where it is difficult or infeasible to develop a conventional algorithm for effectively performing the task. Machine learning is closely related to computational statistics , which focuses on making predictions using computers. The study of mathematical optimization delivers methods, theory and application domains to the field of machine learning. Data mining is a field of study within machine learning, and focuses on exploratory data analysis through unsupervised learning .[3] [4] In its application across business problems, machine learning is also referred to as predictive analytics . Contents 1Overview 1.1Machine learning tasks 2History and relationships to other fields 2.1Relation to data mining 2.2Relation to optimization 2.3Relation to statistics 3Theory 4Approac