How can we compare intelligence of two machines? === The term 'Intelligence' is everywhere! Lots of papers claim an intelligence === How intelligent? Which agent is more intelligent? === E.g. Intelligent decision in stock market The Application of intelligent systems to Financial time series analysis. Forecasting - where computational intelligence meets the stock market An intelligent stock trading decision support system. === Or, would it be better to ask monkey to throw darts? Malkiel: A Random Walk Down Wall Street A monkey throwing darts at the WSJ to select a portfolio might be better than the one carefully selected by experts. => Those machines would be less intelligent than a monkey === Other examples we want to know its intelligence From Deep Blue: beat Kasparov to Watson: won Jeopardy Dr. Fill: joined the human crossword tournamet Siri: incorpolated in i-Phone 4 Essay-scoring software === A degree to how a machine is intelligent Gregory Chaitin (1987), Warren Smith (2006) tried to answer it using complexity theory. Now we have a fair amount of such definitions. === Legg & Hutter's definition From informal An agent's ability to achieve goals in a wide range of environments. to formal \gamma(\pi) = \sum_{\mu \in E} 2^{-K(\mu)} \cdot V_{\mu}^{\pi} === Agent interacts with environment Observation o_i -> Action a_i -> Reward r_i \includegraphics[width=18cm,height=6cm]{env.jpg} yields a history a_1 o_1 r_1... === Definition of agent Function that takes the current history as input and produces an action as output\ \pi(a_3 \vert o_1r_1a_1o_2r_2)$ ... or probability function for indeterministic. === Definition of environment Function which produces output o_k, r_k given the current history $\mu(o_kr_k\vert o_1r_1a_1o_2r_2a_2\cdots o_{k-1}r_{k-1}a_{k-1})$ or probability function for indeterministic. === Expected value of sum of rewards V_{\mu}^{\pi} = E (\sum_{i=1}^{\infty} r_i) after each repetion of o_i -> a_i -> r_i === Definition of intelligence Weighted sum of expected value of sum of rewards over infinite environments \gamma(\pi) = \sum_{\mu \in E} w_{\mu} \cdot V_{\mu}^{\pi} === How will those weights be specified? Translate the environment into a binary string $x$ by Turing Machine U Calculate Kolmogorov complexity K of x (length of the shortest program that computes $x$) $K(x)=\min_p\{l(p) \vert U(p)=x\}$ $w_{\mu}=2^{-K(\mu)}$ The smaller the complexity the larger the weight => Occam's razor === Universal Machine Intelligence by Legg and Hutter \gamma(\pi) = \sum_{\mu \in E} 2^{-K(\mu)} \cdot V_{\mu}^{\pi} ``An agent's ability to achieve goals in a wide range of environments. === Too conceptual or too theoretical Goertzel: "Universal but not practical." === Goertzel: pragmatic intelligence \Pi(\pi) = \sum_{\mu \in E, g \in G, T} ... It's not very practical yet, isn't it? === Problem is, translation of environment by Turing machine Are there easier alternatives to the Turing machine? === Hernandes-Orallo The other representations of environment (i) $\lambda$-calculus, (ii) combinatory logic, (iii) abstract state machines, (iv) register machines, (v) Markov algorithms, (vi) term-rewriting systems, ... to generate environments and calculate complexity automatically. "still Turing-complete, but more natural and easy to work with than the Turing machine. === Hernandes's example tests measures the ability of finding the shortest explanation for some strings of different difficulty in a fixed time” e.g. - x = aaaaaaabaaaaaaaaaaaaaabaaa - x = aabbbccdddeefffgghhhiijjj - x = 1,2,3,5,7,11,13,17,19,23} Still not so practical for our purpose.} === To proceed further (1)}}\\ First, let's be more practical! Let's look for yet another way to measure complexity. === The other ways to measure complexity} although these are not Turing complete any more. Crutchfield et al.: Comment on "Simple Measure for Complexity" $\Gamma_{\alpha \beta} = (S/S_{max})^{\alpha}(1-(S/S_{max}))^{\beta}$ Fioretti: A subjective measure of complexity C_{O}(S) = \sum_{q=0}^{Q} \frac{q+1}{s_q} Lloyd: A survey - Measures of complexity a non-exhaustive list === To proceed further (2)} Second, let's be specific not universal! - "She is an intelligent dancer," while we know she is not good at Mathematics, which we don't care. - This conductor always makes an intelligent interpretation of symphony, but very bad at football. - Would Einstein play tennis intelligently? => Intelligence doesn't need to be universal! === E.g. which route is more intelligent? A business person & a philosopher going for a walk in Manhattan \includegraphics[width=4cm,height=4cm]{trace-96-start-val-1.jpg} \includegraphics[width=4cm,height=4cm]{trace-96-end-new-val-1.jpg} === To proceed further (3) Third, let's be more unpredictable! === What is human-like intelligence? Human-intelligence is spontaneous, flexible, and/or unpredictable, more or less. Or even erroneous sometimes. === A possible trick to the Turing Test might be to give a same question repeatedly. \includegraphics[width=6cm,height=5cm]{turing.jpg} === To mimic a human Do not always exactly the same action even in a same situation. === I beg your pardon? Intelligent people try a different explanation for an easier understanding while others just repeat the same expression, maybe louder. === I couldn't enjoy sushi by a sushi robot! because it tastes always the same. === Why spontaneous? We sometimes need spontaneous and unpredictable intelligence rather than efficiency or effectiveness like in case of SONY's AIBO. It learns excellently and acts differently in different situation but repeats the same action in a same situation. Sooner or later the owners lose their interest === Our modification Legg & Hutter's an ability to achieve goals in a wide range of environment's ability to achieve a goal in an environment + an ability to act differently even in a similar situation === A measure of similarity === Intelligence in a specific domain \gamma(\pi) = \sum_{\mu \in E} 2^{-K(\mu)} \cdot V ... -> repeat a run in a same condition to see similarity \gamma(\pi) = \sum_i \frac{2^{-\{\mbox{\small COMPLEXITY}\}_{i}}\cdot ... === Let's summarize based on Legg & Hutter's definition but specific, not universal more reallistic complexity measure, not by Turing Machine. expect a different action in a same situation. === Is Occam's razor principle really necessary? Occam's razor plays an inportant role but at the same time we doubt it Once Kluger wrote in the TIME Magazine intelligent individuals are more difficult to learn to know. Artificial agents sometimes must pretend to be complex. The issue is still open and many things await to be done. Let's cooperate! === Dziekuje!