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Typical AI these days are question-answering machines. For example, Siri, Alexa and Google Home. But it is always the human asking the questions and the AI answering.
Are there any good examples of an AI that is curious and asks questions of its own accord?
You are referring to 'proactive AI' as opposed to 'reactive AI' like Alexa, Cortana, Siri, Bixby, Google Assistant, and others. There hasn't been much progress in this area of AI. Google's recent demonstration of Duplex addresses this to some extent. Some chatbots are proactive. Genesys provides such capability. Check out their video
Azure's bot service has a page on how to implement proactivity and there is another video that walks through the whole process: Learn to build Proactive Bot in 30 Minutes.
One of the simplest examples that I can think of is "Akinator". At the heart it uses decision trees to narrow down the search. It is not a "questioning" model like QA models used in Alexa, but it does asks questions.
I would like to give you a little bit of a hint,concerning the agents(chat-bots) mentioned in your question body.and also following up the tags and that's strong AI etc.
All the current agents lack comprehension nor reasoning and by this I mean,these agents rely on rule based algorithms, basic neural networks name it... ,they don't exhibit strong "reasoning skills" in that they can be expertly ask questions without training data nor following up human define rules effectively.
Therefore,building up a truly strong nor effective agent requires a lot of time and expertise,which AI research companies lack due to the Artificial Narrow Intelligence level of AI.
So one of the key capabilities which I think to gauge the real AI agent which can as well ask questions effectively is:reasoning and abstraction which will help an agent to autonomously adapt to new situations,and understand nor comprehend the context of the given subject/topic.
Now you can judge according to the above insights, whether we do have good AI that is curious and is definitely accurate in asking questions! Am not criticising the products (chat-bot),these companies put on market but we as scientists in this field,we have to save our civilisation.
Hope this helps.
It's certainly possible to create AI systems that ask questions. Various forms of expert systems and diagnostic support system applications already do that. As to the question of whether or not they are curious, that's one I'll leave to the philosophers. But it is absolutely possible to create an AI that attempts to reason out a solution to a problem, find that it is unable to generate an acceptable answer, and then prompts the user for more information.
One context where this can be done is Abductive Inference systems for medical decision making. I'd refer you to Abductive Inference Models for Diagnostic Problem Solving by Reggia and Peng, or Computer Assisted Medical Decision Making 1 by Reggia and Tuhrim for more on that specific point.
