Traditional Meta-Learning requires long training times, and is often focused on optimizing performance quality, neglecting computational complexity. Algorithm Portfolios are more robust, but present similar limitations. We reformulate algorithm selection as a time allocation problem: all candidate algorithms are run in parallel, and their relative priorities are continually updated based on runtime information, with the aim of minimizing the time to reach a desired performance level. Each algorithm's priority is set based on its current time to solution, estimated according to a parametric model that is trained and used while solving a sequence of problems, gradually increasing its impact on the priority attribution. The use of

The Bayesian framework is a well-studied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard statistical guidelines for choosing the model class and prior are not always available or can fail, in particular in complex situations. Solomonoff completed the Bayesian framework by providing a rigorous, unique, formal, and universal choice for the model class and the prior. I discuss in breadth how and in which sense universal (non-i.i.d.) sequence prediction solves various (philosophical) problems of traditional Bayesian sequence prediction. I show that Solomonoff’s model possesses many desirable properties: Strong total and future bounds, and weak instantaneous bounds, and in contrast to most classical continuous prior densities has no zero p(oste)rior problem, i.e. can confirm universal hypotheses, is reparametrization and regrouping invariant, and avoids the old-evidence and updating problem. It even performs well

The Push programming language was developed for use in genetic and evolutionary computation systems, as the representation within which evolving programs are expressed. It has been used in the production of several significant results, including results that were awarded a gold medal in the Human Competitive Results competition at GECCO-2004. One of Push’s attractive features in this context is its transparent support for the expression and evolution of modular architectures and complex control structures, achieved through explicit code self-manipulation. The latest version of Push, Push3, enhances this feature by permitting explicit manipulation of an execution stack that contains the expressions that are queued for execution in the interpreter. This paper provides a brief introduction to Push and to execution stack manipulation in Push3. It then presents a series of examples in which Push3 was used with a simple genetic programming system (PushGP) to evolve programs with non-trivial control structures.

Artificial intelligence; algorithmic probability; sequential decision theory; rational

We describe an approach to the inductive synthesis of recursive equations from input/outputexamples which is based on the classical two-step approach to induction of functional Lisp programs of Summers (1977). In a first step, I/O-examples are rewritten to traces which explain the outputs given the respective inputs based on a datatype theory. These traces can be integrated into one conditional expression which represents a non-recursive program.

An old dream of computer scientists is to build an optimally ecient universal problem solver. We show how to solve arbitrary computational problems in an optimal fashion inspired by Kurt Godel's celebrated self-referential formulas (1931). Our Godel machine's initial software includes an axiomatic description of: the Godel machine's hardware, the problem-speci c utility function (such as the expected future reward of a robot), known aspects of the environment, costs of actions and computations, and the initial software itself (this is possible without introducing circularity). It also includes a typically sub-optimal initial problem-solving policy and an asymptotically optimal proof searcher searching the space of computable proof techniques|that is, programs whose outputs are proofs. Unlike previous approaches, the self-referential Godel machine will rewrite any part of its software, including axioms and proof searcher, as soon as it has found a proof that this will improve its future performance, given its typically limited computational resources. We show that self-rewrites are globally optimal|no local minima!|since provably none of all the alternative rewrites and proofs (those that could be found by continuing the proof search) are worth waiting for.

Solomonoff completed the Bayesian framework by providing a rigorous, unique, formal, and universal choice for the model class and the prior. We discuss in breadth how and in which sense universal (non-i.i.d.) sequence prediction solves various (philosophical) problems of traditional Bayesian sequence prediction. We show that Solomonoff’s model possesses many desirable properties: Fast convergence and strong bounds, and in contrast to most classical continuous prior densities has no zero p(oste)rior problem, i.e. can confirm universal hypotheses, is reparametrization and regrouping invariant, and avoids the old-evidence and updating problem. It even performs well (actually better) in non-computable environments.

We will describe recent developments in a system for machine learning that we've been working on for some time (Sol 86, Sol 89). It is meant to be a "Scientist's Assistant" of great power and versatility in many areas of science and mathematics. It di#ers from other ambitious work in this area in that we are not so much interested in knowledge itself, as we are in how it is acquired - how machines may learn. To start o#, the system will learn to solve two very general kinds of problems. Most, but perhaps not all problems in science and engineering are of these two kinds.

Given is a problem sequence and a probability distribution (the bias) on programs computing solution candidates. We present an optimally fast way of incrementally solving each task in the sequence. Bias shifts are computed by program prefixes that modify the distribution on their suffixes by reusing successful code for previous tasks (stored in non-modifiable memory). No tested program gets more runtime than its probability times the total search time. In illustrative experiments, ours becomes the first general system to learn a universal solver for arbitrary disk Towers of Hanoi tasks (minimal solution size 2^n - 1). It demonstrates the advantages of incremental learning by profiting from previously solved, simpler tasks involving samples of a simple context free language.

Most traditional artificial intelligence (AI) systems of the past 50 years are either very limited, or based on heuristics, or both. The new millennium, however, has brought substantial progress in the field of theoretically optimal and practically feasible algorithms for prediction, search, inductive inference based on Occam's razor, problem solving, decision making, and reinforcement learning in environments of a very general type. Since inductive inference is at the heart of all inductive sciences, some of the results are relevant not only for AI and computer science but also for physics, provoking nontraditional predictions based on Zuse's thesis of the computer-generated universe.